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Tf 6.23 0 Td (2)Tj /T1_2 10.96 Tf 9.73 0 Td ([)Tj /T1_3 10.96 Tf 3.03 0 Td (\241)Tj /T1_4 10.96 Tf 8.51 0 Td (T)Tj /T1_5 10.96 Tf 6.68 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (T)Tj /T1_2 10.96 Tf 7.48 0 Td (])Tj /T1_4 8.11 Tf 3.04 4.52 Td (d)Tj /T1_5 10.96 Tf 4.97 -4.52 Td (:)Tj /T1_1 10.96 Tf -199.31 -41.31 Td [(W)79(e)-489(denote)-490(by)]TJ /T1_4 10.96 Tf 70.6 0 Td [(su)-75(p)-75(p)]TJ /T1_2 10.96 Tf 22.34 0 Td (\()Tj /T1_4 10.96 Tf 5.89 0 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_2 10.96 Tf 3.3 1.64 Td (\))Tj /T1_1 10.96 Tf 9.62 0 Td [(the)-490(support)-490(of)]TJ /T1_4 10.96 Tf 73.13 0 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_1 10.96 Tf 8.67 1.64 Td [(for)-490(each)]TJ /T1_4 10.96 Tf -200.06 -12.54 Td (t)Tj /T1_3 10.96 Tf 6.22 0 Td (2)Tj /T1_2 10.96 Tf 9.73 0 Td ([)Tj /T1_3 10.96 Tf 3.04 0 Td (\241)Tj /T1_4 10.96 Tf 8.51 0 Td (T)Tj /T1_5 10.96 Tf 6.67 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (T)Tj /T1_2 10.96 Tf 7.49 0 Td (])Tj /T1_4 8.11 Tf 3.03 3.98 Td (d)Tj /T1_1 10.96 Tf 7.71 -3.98 Td [(and)-250(assume)-250(that)]TJ /T1_6 9.86 Tf 11.8 -16.29 Td ([)Tj /T1_4 8.11 Tf -12.55 -23.49 Td (t)Tj /T1_3 8.11 Tf 2.81 0 Td (2)Tj /T1_2 8.11 Tf 5.4 0 Td ([)Tj /T1_3 8.11 Tf 2.24 0 Td (\241)Tj /T1_4 8.11 Tf 6.3 0 Td (T)Tj /T1_5 8.11 Tf 4.94 0 Td (;)Tj /T1_4 8.11 Tf 2.24 0 Td (T)Tj /T1_2 8.11 Tf 5.54 0 Td (])Tj /T1_4 6.57 Tf 2.25 2.34 Td (d)Tj /T1_4 10.96 Tf 5.34 11.51 Td [(su)-75(p)-75(p)]TJ /T1_2 10.96 Tf 22.34 0 Td (\()Tj /T1_4 10.96 Tf 5.89 0 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.65 Td (t)Tj /T1_2 10.96 Tf 3.3 1.65 Td (\))Tj /T1_3 10.96 Tf 6.69 0 Td (\275)Tj /T1_2 10.96 Tf 10.95 0 Td ([)Tj /T1_3 10.96 Tf 3.03 0 Td (\241)Tj /T1_4 10.96 Tf 8.51 0 Td (A)Tj /T1_5 10.96 Tf 6.7 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (A)Tj /T1_2 10.96 Tf 6.69 0 Td (])Tj /T1_4 8.11 Tf 3.04 4.52 Td (d)Tj /T1_1 10.96 Tf -177.2 -42.28 Td [(for)-250(an)]TJ /T1_4 10.96 Tf 28.59 0 Td (A)Tj /T1_5 10.96 Tf 9.13 0 Td (>)Tj /T1_1 10.96 Tf 10.95 0 Td (0)Tj 5.48 0 Td [(.)-249(Then)]TJ /T1_4 10.96 Tf 30.73 0 Td (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_3 10.96 Tf 4.25 0 Td (\242)Tj /T1_2 10.96 Tf 3.04 0 Td (\))Tj /T1_1 10.96 Tf 6.99 0 Td [(can)-249(be)-250(written)-250(as)]TJ /T1_4 10.96 Tf -79.76 -29 Td (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td [(\))-221(=)]TJ /T1_6 9.86 Tf 26.25 13.69 Td (Z)Tj /T1_2 8.11 Tf -10.8 -30.6 Td ([)Tj /T1_3 8.11 Tf 2.24 0 Td (\241)Tj /T1_4 8.11 Tf 6.3 0 Td (A)Tj /T1_5 8.11 Tf 4.95 0 Td (;)Tj /T1_4 8.11 Tf 2.25 0 Td (A)Tj /T1_2 8.11 Tf 4.95 0 Td (])Tj /T1_4 6.57 Tf 2.25 2.35 Td (d)Tj /T1_4 10.96 Tf 9.17 14.56 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_2 10.96 Tf 3.3 1.64 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (x)Tj /T1_2 10.96 Tf 4.9 0 Td (\))Tj /T1_4 10.96 Tf 4.25 0 Td (M)Tj /T1_2 10.96 Tf 9.57 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td [(d)-51(x)]TJ /T1_2 10.96 Tf 10.94 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_4 10.96 Tf 14.94 0 Td (t)Tj /T1_3 10.96 Tf 6.22 0 Td (2)Tj /T1_2 10.96 Tf 9.73 0 Td ([)Tj /T1_3 10.96 Tf 3.04 0 Td (\241)Tj /T1_4 10.96 Tf 8.51 0 Td (T)Tj /T1_5 10.96 Tf 6.67 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (T)Tj /T1_2 10.96 Tf 7.49 0 Td (])Tj /T1_4 8.11 Tf 3.03 4.53 Td (d)Tj /T1_5 10.96 Tf 4.97 -4.53 Td (:)Tj /T1_1 10.96 Tf -207.85 -49 Td [(F)14(or)-237(an)14(y)-238(natural)-239(number)]TJ /T1_4 10.96 Tf 105.07 0 Td (n)Tj /T1_3 10.96 Tf 7.79 0 Td (\270)Tj /T1_1 10.96 Tf 10.84 0 Td (1)Tj 8.09 0 Td (and)Tj /T1_4 10.96 Tf 18.44 0 Td (k)Tj /T1_2 10.96 Tf 7.37 0 Td [(=)-210(\()]TJ /T1_4 10.96 Tf 15.08 0 Td (k)Tj /T1_1 8.11 Tf 4.86 -1.65 Td (1)Tj /T1_5 10.96 Tf 4.56 1.65 Td [(;)-109(:::)1(;)]TJ /T1_4 10.96 Tf 17.6 0 Td (k)Tj /T1_4 8.11 Tf 4.87 -1.81 Td (d)Tj /T1_2 10.96 Tf 4.97 1.81 Td (\))Tj /T1_3 10.96 Tf 6.57 0 Td (2)Tj /T1_7 10.96 Tf 9.62 0 Td (Z)Tj /T1_4 8.11 Tf 7.3 3.98 Td (d)Tj /T1_1 10.96 Tf -233.03 -16.52 Td (with)Tj /T1_3 10.96 Tf 22.22 0 Td (\241)Tj /T1_4 10.96 Tf 8.51 0 Td (n)Tj /T1_3 10.96 Tf 7.91 0 Td (\267)Tj /T1_4 10.96 Tf 10.95 0 Td (k)Tj /T1_1 8.11 Tf 4.87 -1.65 Td (1)Tj /T1_5 10.96 Tf 4.55 1.65 Td [(;)-110(::)1(:)1(;)]TJ /T1_4 10.96 Tf 17.6 0 Td (k)Tj /T1_4 8.11 Tf 4.87 -1.81 Td (d)Tj /T1_5 10.96 Tf 7.41 1.81 Td (<)Tj /T1_4 10.96 Tf 10.94 0 Td (n)Tj /T1_1 10.96 Tf 5.48 0 Td [(,)-250(let)]TJ /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 162.3948 473.1085 Tm -90.98 -30.57 Td (x)Tj /T1_4 8.11 Tf 1.0003 0 0 1.0003 66.2784 442.5301 Tm 5.4 -1.82 Td (k)Tj /T1_2 10.96 Tf 6.67 1.82 Td (=)Tj /T1_6 10.96 Tf 10.94 15.45 Td (\265)Tj /T1_4 10.96 Tf 8.07 -15.45 Td (k)Tj /T1_1 8.11 Tf 4.86 -1.66 Td (1)Tj /T1_4 10.96 Tf 5.75 9.07 Td (A)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 0 G 0.44 w 10 M 0 j 0 J []0 d 35.97 -324.54 m 42.67 -324.54 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_4 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 36.58 -334.79 Td (n)Tj /T1_5 10.96 Tf 7.28 7.52 Td (;)Tj /T1_3 10.96 Tf 4.25 0 Td [(\242)-110(\242)-110(\242)]TJ /T1_5 10.96 Tf 13.98 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (k)Tj /T1_4 8.11 Tf 4.86 -1.82 Td (d)Tj /T1_4 10.96 Tf 6.17 9.23 Td (A)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 77.37 -324.54 m 84.07 -324.54 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_4 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 77.98 -334.79 Td (n)Tj /T1_6 10.96 Tf 7.28 22.97 Td (\266)Tj /T1_5 10.96 Tf 9.28 -15.45 Td (;)Tj /T1_9 10.96 Tf -100.26 -30.27 Td (D)Tj /T1_4 8.11 Tf 6.7 -1.81 Td (k)Tj /T1_2 10.96 Tf 6.67 1.81 Td (=)Tj /T1_6 10.96 Tf 10.95 15.45 Td (\267)Tj /T1_4 10.96 Tf 5.78 -15.45 Td (k)Tj /T1_1 8.11 Tf 4.86 -1.66 Td (1)Tj /T1_4 10.96 Tf 5.75 9.08 Td (A)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 34.99 -354.8 m 41.68 -354.8 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_4 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 35.59 -365.06 Td (n)Tj /T1_5 10.96 Tf 7.29 7.52 Td (;)Tj /T1_2 10.96 Tf 4.25 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (k)Tj /T1_1 8.11 Tf 4.86 -1.66 Td (1)Tj /T1_2 10.96 Tf 6.08 1.66 Td (+)Tj /T1_1 10.96 Tf 10.03 0 Td (1)Tj /T1_2 10.96 Tf 5.48 0 Td (\))Tj /T1_4 10.96 Tf 5.44 7.42 Td (A)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 83.27 -354.8 m 89.97 -354.8 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_4 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 83.88 -365.06 Td (n)Tj /T1_6 10.96 Tf 7.28 22.97 Td (\266)Tj /T1_3 10.96 Tf 9.59 -15.45 Td [(\243)-137(\242)-111(\242)-110(\242)-138(\243)]TJ /T1_6 10.96 Tf 33.13 15.45 Td (\267)Tj /T1_4 10.96 Tf 5.77 -15.45 Td (k)Tj /T1_4 8.11 Tf 4.86 -1.81 Td (d)Tj /T1_4 10.96 Tf 6.17 9.23 Td (A)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 150.68 -354.8 m 157.38 -354.8 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_4 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 151.29 -365.06 Td (n)Tj /T1_5 10.96 Tf 7.28 7.52 Td (;)Tj /T1_2 10.96 Tf 4.25 0 Td (\()Tj /T1_4 10.96 Tf 4.26 0 Td (k)Tj /T1_4 8.11 Tf 4.86 -1.81 Td (d)Tj /T1_2 10.96 Tf 6.49 1.81 Td (+)Tj /T1_1 10.96 Tf 10.04 0 Td (1)Tj /T1_2 10.96 Tf 5.48 0 Td (\))Tj /T1_4 10.96 Tf 5.44 7.42 Td (A)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 199.39 -354.8 m 206.09 -354.8 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_4 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 200 -365.06 Td (n)Tj /T1_6 10.96 Tf 7.28 22.97 Td (\266)Tj /T1_5 10.96 Tf 9.28 -15.45 Td (:)Tj /T1_1 10.96 Tf -231.5 -37.29 Td [(W)79(e)-249(de\002ne)-250(the)-250(step)-250(function)]TJ 61.15 -24.38 Td (\230)Tj /T1_4 10.96 Tf -1.32 -2.43 Td (f)Tj /T1_2 8.11 Tf 4.64 5.79 Td (\()Tj /T1_4 8.11 Tf 3.15 0 Td (n)Tj /T1_2 8.11 Tf 4.05 0 Td (\))Tj /T1_4 8.11 Tf -8.73 -8.17 Td (t)Tj /T1_2 10.96 Tf 12.38 2.38 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (x)Tj /T1_2 10.96 Tf 4.89 0 Td (\))Tj /T1_1 10.96 Tf 6.69 0 Td (:)Tj /T1_2 10.96 Tf 3.04 0 Td (=)Tj /T1_9 15.78 Tf 14.62 -2.34 Td (\345)Tj /T1_3 8.11 Tf -3.67 -9.54 Td (j)Tj /T1_4 8.11 Tf 2.25 0 Td (k)Tj /T1_3 8.11 Tf 3.74 0 Td [(j)1(\267)]TJ /T1_4 8.11 Tf 8.54 0 Td (n)Tj /T1_4 10.96 Tf 6.91 11.88 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.65 Td (t)Tj /T1_2 10.96 Tf 3.3 1.65 Td (\()Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 190.0924 348.1342 Tm 4.26 0 Td (x)Tj /T1_4 8.11 Tf 1.0003 0 0 1.0003 194.3536 348.1342 Tm 5.4 -1.81 Td (k)Tj /T1_2 10.96 Tf 4.23 1.81 Td (\))Tj /T1_1 10.96 Tf 4.25 0 Td [(1)258(I)]TJ /T1_9 8.11 Tf 6.29 -1.77 Td (D)Tj /T1_4 6.57 Tf 4.97 -1.74 Td (k)Tj /T1_2 10.96 Tf 4.02 3.51 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (x)Tj /T1_2 10.96 Tf 4.9 0 Td (\))Tj /T1_1 10.96 Tf -175.57 -35.7 Td [(to)-573(approximate)]TJ /T1_4 10.96 Tf 77.5 0 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.65 Td (t)Tj /T1_1 10.96 Tf 3.3 1.65 Td [(,)-574(where)]TJ /T1_3 10.96 Tf 42.08 0 Td (j)Tj /T1_4 10.96 Tf 3.03 0 Td (k)Tj /T1_3 10.96 Tf 5.06 0 Td [(j)-400(\267)]TJ /T1_4 10.96 Tf 20.35 0 Td (n)Tj /T1_1 10.96 Tf 11.76 0 Td [(is)-573(meant)-574(to)-574(be)]TJ -166.2 -12.55 Td [(componentwise,)-244(i.)-243(e.)]TJ /T1_3 10.96 Tf 92.92 0 Td (\241)Tj /T1_4 10.96 Tf 8.51 0 Td (n)Tj /T1_3 10.96 Tf 7.85 0 Td (\267)Tj /T1_4 10.96 Tf 10.89 0 Td (k)Tj /T1_4 8.11 Tf 4.86 -1.64 Td (i)Tj /T1_5 10.96 Tf 5.13 1.64 Td (<)Tj /T1_4 10.96 Tf 10.88 0 Td (n)Tj /T1_1 10.96 Tf 8.15 0 Td (for)Tj /T1_4 10.96 Tf 15.45 0 Td (i)Tj /T1_2 10.96 Tf 5.42 0 Td (=)Tj /T1_1 10.96 Tf 10.89 0 Td (1)Tj /T1_5 10.96 Tf 5.47 0 Td [(;)-110(:::)1(;)]TJ /T1_4 10.96 Tf 17.61 0 Td (d)Tj /T1_1 10.96 Tf 6.05 0 Td [(.)-243(Then)]TJ -210.08 -12.54 Td [(we)-250(ha)19(v)15(e)]TJ 9.98 -24.23 Td (\230)Tj /T1_4 10.96 Tf -2.59 -2.18 Td (X)Tj /T1_2 8.11 Tf 7.73 4.52 Td (\()Tj /T1_4 8.11 Tf 3.14 0 Td (n)Tj /T1_2 8.11 Tf 4.06 0 Td (\))Tj /T1_2 10.96 Tf 3.64 -4.52 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td [(\))-221(=)]TJ /T1_6 9.86 Tf 26.25 13.69 Td (Z)Tj /T1_2 8.11 Tf -10.8 -30.6 Td ([)Tj /T1_3 8.11 Tf 2.24 0 Td (\241)Tj /T1_4 8.11 Tf 6.3 0 Td (A)Tj /T1_5 8.11 Tf 4.95 0 Td (;)Tj /T1_4 8.11 Tf 2.25 0 Td (A)Tj /T1_2 8.11 Tf 4.95 0 Td (])Tj /T1_4 6.57 Tf 2.25 2.34 Td (d)Tj /T1_1 10.96 Tf 10.49 17 Td (\230)Tj /T1_4 10.96 Tf -1.32 -2.43 Td (f)Tj /T1_2 8.11 Tf 4.65 5.8 Td (\()Tj /T1_4 8.11 Tf 3.14 0 Td (n)Tj /T1_2 8.11 Tf 4.06 0 Td (\))Tj /T1_4 8.11 Tf -8.73 -8.18 Td (t)Tj /T1_2 10.96 Tf 12.37 2.38 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (x)Tj /T1_2 10.96 Tf 4.9 0 Td (\))Tj /T1_4 10.96 Tf 4.25 0 Td (M)Tj /T1_2 10.96 Tf 9.56 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td [(d)-52(x)]TJ /T1_2 10.96 Tf 10.95 0 Td [(\))-221(=)]TJ /T1_9 15.78 Tf 21.3 -2.34 Td (\345)Tj /T1_3 8.11 Tf -3.67 -9.54 Td (j)Tj /T1_4 8.11 Tf 2.25 0 Td (k)Tj /T1_3 8.11 Tf 3.73 0 Td (j\267)Tj /T1_4 8.11 Tf 8.55 0 Td (n)Tj /T1_4 10.96 Tf 6.91 11.88 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_2 10.96 Tf 3.3 1.64 Td (\()Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 237.5355 260.9102 Tm 4.25 0 Td (x)Tj /T1_4 8.11 Tf 1.0003 0 0 1.0003 241.7866 260.9102 Tm 5.4 -1.81 Td (k)Tj /T1_2 10.96 Tf 4.24 1.81 Td (\))Tj /T1_4 10.96 Tf 4.25 0 Td (M)Tj /T1_2 10.96 Tf 9.56 0 Td (\()Tj /T1_9 10.96 Tf 4.26 0 Td (D)Tj /T1_4 8.11 Tf 6.7 -1.81 Td (k)Tj /T1_2 10.96 Tf 4.24 1.81 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (:)Tj /T1_1 10.96 Tf -227.58 -40.82 Td [(In)-395(the)-395(last)-395(sum,)]TJ /T1_4 10.96 Tf 76.05 0 Td (M)Tj /T1_2 10.96 Tf 9.57 0 Td (\()Tj /T1_9 10.96 Tf 4.25 0 Td (D)Tj /T1_4 8.11 Tf 6.7 -1.81 Td (k)Tj /T1_2 10.96 Tf 4.24 1.81 Td (\))Tj /T1_1 10.96 Tf 4.25 0 Td (,)Tj /T1_3 10.96 Tf 7.07 0 Td (j)Tj /T1_4 10.96 Tf 3.03 0 Td (k)Tj /T1_3 10.96 Tf 5.06 0 Td [(j)-301(\267)]TJ /T1_4 10.96 Tf 18.18 0 Td (n)Tj /T1_1 10.96 Tf 5.48 0 Td [(,)-395(are)-395(independent)]TJ /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 200.9754 220.079 Tm 82.65 0 Td (a)Tj /T1_1 10.96 Tf 1.0003 0 0 1.0003 283.6481 220.079 Tm 7.83 0 Td (-)Tj -234.36 -12.54 Td [(stable)-464(random)-465(v)24(ariables)-464(which)-465(can)-464(be)-465(simulated)-465(as)]TJ T* [(presented)-250(in)-250(Chambers)]TJ /T1_4 10.96 Tf 103.15 0 Td [(et)-249(al.)]TJ /T1_1 10.96 Tf 24.65 0 Td (\(1976\).)Tj -127.8 -19.39 Td [(The)-600(follo)24(wing)-599(theorem)-600(pro)14(vides)-599(error)-600(bounds)-601(for)]TJ /T1_4 10.96 Tf T* [(E)-73(r)-23(r)]TJ /T1_2 10.96 Tf 16.52 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_2 10.96 Tf 7.73 0 Td (\()Tj /T1_4 10.96 Tf 3.97 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_1 10.96 Tf 6.84 2.18 Td (\230)Tj /T1_4 10.96 Tf -2.58 -2.18 Td (X)Tj /T1_2 8.11 Tf 7.72 3.98 Td (\()Tj /T1_4 8.11 Tf 3.15 0 Td (n)Tj /T1_2 8.11 Tf 4.05 0 Td (\))Tj /T1_2 10.96 Tf 3.64 -3.98 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\)\))Tj /T1_1 10.96 Tf 11.24 0 Td [(for)-250(H)]TJ 24.34 0.06 Td (\250)Tj -0.92 -0.06 Td [(older)19(-continuous)-249(functions)]TJ /T1_4 10.96 Tf 121.93 0 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_1 10.96 Tf 3.3 1.64 Td (.)Tj -234.11 -28.48 Td [(Theorem)-250(1)]TJ /T1_4 10.96 Tf T* [(Assume)-385(that)]TJ /T1_1 10.96 Tf 58.95 0 Td (0)Tj /T1_5 10.96 Tf 8.74 0 Td (<)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 124.7645 122.0221 Tm 11.77 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 136.5377 122.0221 Tm 11.08 0 Td (\267)Tj /T1_1 10.96 Tf 11.77 0 Td (2)Tj /T1_4 10.96 Tf 5.48 0 Td (,)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 164.8755 122.0221 Tm 6.95 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 171.8274 122.0221 Tm 11.08 0 Td (6)Tj /T1_2 10.96 Tf (=)Tj /T1_1 10.96 Tf 11.77 0 Td (1)Tj /T1_4 10.96 Tf 9.7 0 Td [(and)-385(the)-385(functions)]TJ 84.3 0 Td (f)Tj /T1_4 8.11 Tf 3.11 -1.64 Td (t)Tj /T1_4 10.96 Tf -234.7 -10.9 Td [(ar)36(e)-421(H)]TJ 27.63 -0.07 Td (\250)Tj -0.89 0.07 Td [(older)20(-continuous)-422(for)-422(all)]TJ 112.6 0 Td (t)Tj /T1_3 10.96 Tf 7.28 0 Td (2)Tj /T1_2 10.96 Tf 10.78 0 Td ([)Tj /T1_3 10.96 Tf 3.03 0 Td (\241)Tj /T1_4 10.96 Tf 8.52 0 Td (T)Tj /T1_5 10.96 Tf 6.67 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (T)Tj /T1_2 10.96 Tf 7.48 0 Td (])Tj /T1_4 8.11 Tf 3.04 3.98 Td (d)Tj /T1_4 10.96 Tf 4.97 -3.98 Td [(,)-422(i.)-423(e)14(.)-422(for)]TJ -195.36 -12.54 Td (x)Tj /T1_5 10.96 Tf 4.9 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (y)Tj /T1_3 10.96 Tf 7.3 0 Td (2)Tj /T1_2 10.96 Tf 9.73 0 Td ([)Tj /T1_3 10.96 Tf 3.03 0 Td (\241)Tj /T1_4 10.96 Tf 8.52 0 Td (A)Tj /T1_5 10.96 Tf 6.69 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (A)Tj /T1_2 10.96 Tf 6.7 0 Td (])Tj /T1_4 8.11 Tf 3.03 3.97 Td (d)Tj /T1_4 10.96 Tf 4.97 -3.97 Td [(,)-250(it)-250(holds)]TJ /T1_3 10.96 Tf -45.04 -25.42 Td (j)Tj /T1_4 10.96 Tf 4.68 0 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_2 10.96 Tf 3.3 1.64 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (x)Tj /T1_2 10.96 Tf 4.9 0 Td (\))Tj /T1_3 10.96 Tf 5.77 0 Td (\241)Tj /T1_4 10.96 Tf 11.68 0 Td (f)Tj /T1_4 8.11 Tf 3.11 -1.64 Td (t)Tj /T1_2 10.96 Tf 3.31 1.64 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (y)Tj /T1_2 10.96 Tf 4.86 0 Td (\))Tj /T1_3 10.96 Tf 4.25 0 Td [(j)-221(\267)]TJ /T1_4 10.96 Tf 15.87 0 Td (C)Tj /T1_4 8.11 Tf 6.83 -1.64 Td (t)Tj /T1_3 10.96 Tf 4.83 1.64 Td [(\242)-137(jj)]TJ /T1_4 10.96 Tf 10.62 0 Td (x)Tj /T1_3 10.96 Tf 6.42 0 Td (\241)Tj /T1_4 10.96 Tf 10.04 0 Td (y)Tj /T1_3 10.96 Tf 4.86 0 Td (jj)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 192.373 71.5082 Tm 5.13 5.6 Td (g)Tj /T1_4 6.57 Tf 1.0003 0 0 1.0003 198.4447 77.1098 Tm 3.17 -1.22 Td (t)Tj /T1_1 8.11 Tf -3.17 -7.78 Td (2)Tj /T1_5 10.96 Tf 6.44 3.4 Td (;)Tj /T1_4 10.96 Tf 14.94 0 Td (t)Tj /T1_3 10.96 Tf 6.22 0 Td (2)Tj /T1_2 10.96 Tf 9.73 0 Td ([)Tj /T1_3 10.96 Tf 3.04 0 Td (\241)Tj /T1_4 10.96 Tf 8.51 0 Td (T)Tj /T1_5 10.96 Tf 6.67 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (T)Tj /T1_2 10.96 Tf 7.49 0 Td (])Tj /T1_4 8.11 Tf 3.03 4.53 Td (d)Tj /T1_5 10.96 Tf 4.97 -4.53 Td (;)Tj /T1_4 10.96 Tf 38.37 676.28 Td [(for)-209(some)]TJ /T1_1 10.96 Tf 39.88 0 Td (0)Tj /T1_5 10.96 Tf 7.49 0 Td (<)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 359.519 747.974 Tm 10.53 0 Td (g)Tj /T1_4 8.11 Tf 1.0003 0 0 1.0003 370.0518 747.974 Tm 4.3 -1.65 Td (t)Tj /T1_3 10.96 Tf 5.32 1.65 Td (\267)Tj /T1_1 10.96 Tf 10.53 0 Td (1)Tj /T1_4 10.96 Tf 7.76 0 Td (and)Tj 18.18 0 Td (C)Tj /T1_4 8.11 Tf 6.83 -1.65 Td (t)Tj /T1_5 10.96 Tf 5.32 1.65 Td (>)Tj /T1_1 10.96 Tf 10.53 0 Td (0)Tj /T1_4 10.96 Tf 5.47 0 Td [(,)-209(wher)36(e)]TJ /T1_3 10.96 Tf 33.69 0 Td [(k)-100(\242)-100(k)]TJ /T1_1 8.11 Tf 16.2 -1.66 Td (2)Tj /T1_4 10.96 Tf 6.83 1.66 Td [(denotes)-209(the)]TJ -188.86 -12.3 Td [(Euclidean)-213(norm.)-213(Then)-213(for)-213(any)]TJ 132.2 0 Td (t)Tj /T1_3 10.96 Tf 5.85 0 Td (2)Tj /T1_2 10.96 Tf 9.36 0 Td ([)Tj /T1_3 10.96 Tf 3.03 0 Td (\241)Tj /T1_4 10.96 Tf 8.52 0 Td (T)Tj /T1_5 10.96 Tf 6.67 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (T)Tj /T1_2 10.96 Tf 7.48 0 Td (])Tj /T1_4 8.11 Tf 3.04 3.98 Td (d)Tj /T1_4 10.96 Tf 7.3 -3.98 Td [(we)-213(have)-213(for)]TJ -187.7 -12.3 Td (all)Tj 14.31 0 Td (n)Tj /T1_3 10.96 Tf 7.91 0 Td (\270)Tj /T1_1 10.96 Tf 10.95 0 Td (1)Tj /T1_4 10.96 Tf 8.22 0 Td (that)Tj -36.49 -18.74 Td [(E)-73(r)-23(r)]TJ /T1_2 10.96 Tf 16.53 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_1 10.96 Tf 6.84 2.18 Td (\230)Tj /T1_4 10.96 Tf -2.59 -2.18 Td (X)Tj /T1_2 8.11 Tf 7.72 4.52 Td (\()Tj /T1_4 8.11 Tf 3.15 0 Td (n)Tj /T1_2 8.11 Tf 4.05 0 Td (\))Tj /T1_2 10.96 Tf 3.65 -4.52 Td (\()Tj /T1_4 10.96 Tf 3.97 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\)\))Tj /T1_3 10.96 Tf -54.09 -25.51 Td (\267)Tj /T1_4 10.96 Tf 10.4 0 Td (C)Tj /T1_4 8.11 Tf 6.83 -1.65 Td (t)Tj /T1_3 10.96 Tf 4.82 1.65 Td (\242)Tj /T1_1 10.96 Tf 4.56 0 Td (2)Tj /T1_4 8.11 Tf 5.48 4.52 Td (d)Tj /T1_5 8.11 Tf 4.47 0 Td (=)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 370.622 683.6263 Tm 4.06 0 Td (a)Tj /T1_6 10.96 Tf 1.0003 0 0 1.0003 374.6831 683.6263 Tm 7.5 10.93 Td (\265)Tj /T1_4 10.96 Tf 22.46 -8.04 Td (d)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 319.35 -88.02 m 351.81 -88.02 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 319.35 -98.28 Td (1)Tj /T1_2 10.96 Tf 7 0 Td (+)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 398.4396 671.583 Tm 10.04 0 Td [(a)-82(g)]TJ /T1_4 8.11 Tf 1.0003 0 0 1.0003 408.4824 671.583 Tm 12.12 -1.64 Td (t)Tj /T1_6 10.96 Tf 4.5 24.61 Td (\266)Tj /T1_1 8.11 Tf 8.06 -2.7 Td (1)Tj /T1_5 8.11 Tf 4.06 0 Td (=)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 437.2303 691.8586 Tm 4.05 0 Td (a)Tj /T1_4 10.96 Tf 1.0003 0 0 1.0003 441.2814 691.8586 Tm 7.5 -12.75 Td (A)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 448.7834 679.1051 Tm 5.94 4.52 Td (g)Tj /T1_4 6.57 Tf 1.0003 0 0 1.0003 455.4753 683.6263 Tm 3.17 -1.22 Td (t)Tj /T1_2 8.11 Tf 2.77 1.22 Td (+)Tj /T1_4 8.11 Tf 6.3 0 Td (d)Tj /T1_5 8.11 Tf 4.48 0 Td (=)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 472.1999 683.6263 Tm 4.05 0 Td (a)Tj /T1_6 10.96 Tf 1.0003 0 0 1.0003 476.251 683.6263 Tm 7.5 10.93 Td (\265)Tj /T1_1 10.96 Tf 9.26 -8.04 Td (1)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 420.91 -88.02 m 426.39 -88.02 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_4 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 420.91 -98.28 Td (n)Tj /T1_6 10.96 Tf 6.67 22.97 Td (\266)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 499.6974 694.5593 Tm 8.52 -2.7 Td (g)Tj /T1_4 6.57 Tf 1.0003 0 0 1.0003 507.7697 691.8586 Tm 3.16 -1.22 Td (t)Tj /T1_4 10.96 Tf -198.74 -36.88 Td (for)Tj /T1_1 10.96 Tf 15.52 0 Td (0)Tj /T1_5 10.96 Tf 7.92 0 Td (<)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 335.5824 653.7481 Tm 10.94 0 Td (a)Tj /T1_5 10.96 Tf 1.0003 0 0 1.0003 346.5254 653.7481 Tm 10.26 0 Td (<)Tj /T1_1 10.96 Tf 10.95 0 Td (1)Tj /T1_4 10.96 Tf 8.21 0 Td (and)Tj -57.63 -20.3 Td [(E)-72(r)-23(r)]TJ /T1_2 10.96 Tf 16.52 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_1 10.96 Tf 6.84 2.18 Td (\230)Tj /T1_4 10.96 Tf -2.59 -2.18 Td (X)Tj /T1_2 8.11 Tf 7.73 4.52 Td (\()Tj /T1_4 8.11 Tf 3.14 0 Td (n)Tj /T1_2 8.11 Tf 4.06 0 Td (\))Tj /T1_2 10.96 Tf 3.64 -4.52 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td [(\))1(\))]TJ /T1_3 10.96 Tf -54.1 -25.56 Td (\267)Tj /T1_4 10.96 Tf 10.4 0 Td (C)Tj /T1_4 8.11 Tf 6.83 -1.64 Td (t)Tj /T1_3 10.96 Tf 4.83 1.64 Td (\242)Tj /T1_1 10.96 Tf 4.55 0 Td (2)Tj /T1_4 8.11 Tf 5.48 4.53 Td (d)Tj /T1_6 10.96 Tf 6.19 10.93 Td (\265)Tj /T1_4 10.96 Tf 22.47 -8.04 Td (d)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 310.78 -159.23 m 343.24 -159.23 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 310.78 -169.48 Td (1)Tj /T1_2 10.96 Tf 7 0 Td (+)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 389.8673 600.3634 Tm 10.03 0 Td [(a)-83(g)]TJ /T1_4 8.11 Tf 1.0003 0 0 1.0003 399.9 600.3634 Tm 12.13 -1.65 Td (t)Tj /T1_6 10.96 Tf 4.49 24.62 Td (\266)Tj /T1_1 8.11 Tf 8.07 -2.71 Td (1)Tj /T1_5 8.11 Tf 4.05 0 Td (=)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 428.6479 620.629 Tm 4.05 0 Td (a)Tj /T1_4 10.96 Tf 1.0003 0 0 1.0003 432.6991 620.629 Tm 7.51 -12.75 Td (A)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 440.2111 607.8755 Tm 5.94 4.53 Td (g)Tj /T1_4 6.57 Tf 1.0003 0 0 1.0003 446.9129 612.4068 Tm 3.16 -1.22 Td (t)Tj /T1_2 8.11 Tf 2.78 1.22 Td (+)Tj /T1_4 8.11 Tf 6.29 0 Td (d)Tj /T1_5 8.11 Tf 4.48 0 Td (=)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 463.6275 612.4068 Tm 4.05 0 Td (a)Tj /T1_6 10.96 Tf 1.0003 0 0 1.0003 467.6786 612.4068 Tm 7.51 10.93 Td (\265)Tj /T1_1 10.96 Tf 9.26 -8.04 Td (1)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 412.33 -159.23 m 417.81 -159.23 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_4 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 412.33 -169.48 Td (n)Tj /T1_6 10.96 Tf 6.68 22.97 Td (\266)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 491.1251 623.3398 Tm 8.51 -2.71 Td (g)Tj /T1_4 6.57 Tf 1.0003 0 0 1.0003 499.1873 620.629 Tm 3.17 -1.21 Td (t)Tj /T1_2 8.11 Tf 2.77 1.21 Td (+)Tj /T1_4 8.11 Tf 6.3 0 Td (d)Tj /T1_2 8.11 Tf 4.48 0 Td (\()Tj /T1_1 8.11 Tf 3.14 0 Td (1)Tj /T1_5 8.11 Tf 4.06 0 Td (=)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 523.1139 620.629 Tm 4.05 0 Td (a)Tj /T1_3 8.11 Tf 1.0003 0 0 1.0003 527.165 620.629 Tm 5.79 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (1)Tj /T1_2 8.11 Tf 4.05 0 Td (\))Tj /T1_4 10.96 Tf -231.11 -38.09 Td (for)Tj /T1_1 10.96 Tf 15.53 0 Td (1)Tj /T1_5 10.96 Tf 7.91 0 Td (<)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 335.5824 582.5285 Tm 10.95 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 346.5354 582.5285 Tm 10.25 0 Td (\267)Tj /T1_1 10.96 Tf 10.95 0 Td (2)Tj /T1_4 10.96 Tf 5.48 0 Td (.)Tj /T1_1 10.96 Tf -61.07 -34.46 Td [(As)-474(a)-475(consequence,)-475(for)]TJ 109.33 0 Td (0)Tj /T1_5 10.96 Tf 9.28 0 Td (<)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 430.7785 548.0591 Tm 12.31 0 Td (a)Tj /T1_5 10.96 Tf 1.0003 0 0 1.0003 443.0919 548.0591 Tm 11.63 0 Td (<)Tj /T1_1 10.96 Tf 12.31 0 Td (1)Tj 10.68 0 Td [(the)-474(error)-475(bound)]TJ -165.54 -12.3 Td [(con)39(v)15(er)18(ges)-266(to)-267(zero)-268(as)]TJ /T1_4 10.96 Tf 91.84 0 Td (n)Tj /T1_1 10.96 Tf 8.4 0 Td [(goes)-267(to)-267(in\002nity)64(.)-267(F)14(or)]TJ 89.06 0 Td (1)Tj /T1_5 10.96 Tf 8.02 0 Td (<)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 509.5101 535.7557 Tm 11.05 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 520.5632 535.7557 Tm 10.37 0 Td (\267)Tj /T1_1 10.96 Tf 11.05 0 Td (2)Tj 5.48 0 Td (,)Tj -235.27 -12.3 Td [(the)-248(condition)]TJ /T1_4 10.96 Tf 60.23 0 Td (d)Tj /T1_5 10.96 Tf 8.46 0 Td (<)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 380.8448 523.4523 Tm 13.46 5.23 Td [(a)-83(g)]TJ /T1_4 6.57 Tf 1.0003 0 0 1.0003 395.1787 528.6838 Tm 8.96 -1.22 Td (t)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 320.89 -243.63 m 337.03 -243.63 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 72 769.89 Tm 362.66 -250.15 Td (a)Tj /T1_3 8.11 Tf 1.0003 0 0 1.0003 392.9681 519.6713 Tm 5.79 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (1)Tj /T1_1 10.96 Tf 7.97 3.78 Td [(has)-248(to)-249(be)-248(full\002lled)-249(to)-248(get)-249(such)-248(a)]TJ -100.88 -12.3 Td [(con)39(v)15(er)18(gence.)]TJ 0 -28.23 TD [(Remark)-250(2)]TJ /T1_4 10.96 Tf 0 -12.3 TD [(Suppose)-378(that)-378(the)-379(conditions)-378(of)-378(Theor)36(em)-377(1)-379(hold)-378(true)14(.)]TJ T* [(If)-401(the)-402(support)-401(of)]TJ 81.32 0 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_4 10.96 Tf 7.7 1.64 Td [(is)-401(not)-401(compact,)-402(we)-401(\002r)9(st)-401(need)-401(to)]TJ -92.14 -12.3 Td (estimate)Tj 71.68 -14.84 Td (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td [(\))-221(=)]TJ /T1_6 9.86 Tf 17.63 13.68 Td (Z)Tj /T1_4 8.11 Tf -1.8 -30.59 Td (R)Tj /T1_4 6.57 Tf 4.95 2.34 Td (d)Tj /T1_4 10.96 Tf 9.55 14.57 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.65 Td (t)Tj /T1_2 10.96 Tf 3.3 1.65 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (x)Tj /T1_2 10.96 Tf 4.9 0 Td (\))Tj /T1_4 10.96 Tf 4.25 0 Td (M)Tj /T1_2 10.96 Tf 9.57 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td [(d)-51(x)]TJ /T1_2 10.96 Tf 10.94 0 Td (\))Tj /T1_4 10.96 Tf -162.08 -30.72 Td (by)Tj 59.64 -16.95 Td (X)Tj /T1_4 8.11 Tf 6.42 -1.64 Td (K)Tj /T1_2 10.96 Tf 6.35 1.64 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td [(\))-221(=)]TJ /T1_6 9.86 Tf 27.15 13.69 Td (Z)Tj /T1_2 8.11 Tf -11.7 -30.6 Td ([)Tj /T1_3 8.11 Tf 2.24 0 Td (\241)Tj /T1_4 8.11 Tf 6.3 0 Td (K)Tj /T1_5 8.11 Tf 5.86 0 Td (;)Tj /T1_4 8.11 Tf 2.24 0 Td (K)Tj /T1_2 8.11 Tf 5.85 0 Td (])Tj /T1_4 6.57 Tf 2.25 2.34 Td (d)Tj /T1_4 10.96 Tf 9.17 14.57 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_2 10.96 Tf 3.3 1.64 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (x)Tj /T1_2 10.96 Tf 4.9 0 Td (\))Tj /T1_4 10.96 Tf 4.25 0 Td (M)Tj /T1_2 10.96 Tf 9.57 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td [(d)-51(x)]TJ /T1_2 10.96 Tf 10.94 0 Td (\))Tj /T1_4 10.96 Tf -174.12 -32.75 Td [(F)104(or)]TJ 19.48 0 Td (K)Tj /T1_5 10.96 Tf 11.16 0 Td (>)Tj /T1_1 10.96 Tf 11.75 0 Td (0)Tj /T1_4 10.96 Tf 9.68 0 Td [(lar)37(g)10(e)-382(enough,)-383(the)-383(appr)44(oximation)-382(err)44(or)-382(is)]TJ -52.07 -12.3 Td [(small)-250(since)]TJ 12.82 -36.24 Td [(E)-72(r)-23(r)]TJ /T1_2 10.96 Tf 16.52 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_4 8.11 Tf 6.42 -1.64 Td (K)Tj /T1_2 10.96 Tf 6.35 1.64 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td [(\)\))-220(=)]TJ /T1_6 10.96 Tf 21.89 25.31 Td (0)Tj 0 -19.28 TD (B)Tj 0 -7 TD (@)Tj /T1_6 9.86 Tf 28.85 14.66 Td (Z)Tj /T1_7 8.11 Tf -18.72 -30.6 Td (R)Tj /T1_4 6.57 Tf 5.86 2.35 Td (d)Tj /T1_3 8.11 Tf 4.13 -2.35 Td (n)Tj /T1_2 8.11 Tf 4.05 0 Td ([)Tj /T1_3 8.11 Tf 2.25 0 Td (\241)Tj /T1_4 8.11 Tf 6.3 0 Td (K)Tj /T1_5 8.11 Tf 5.85 0 Td (;)Tj /T1_4 8.11 Tf 2.24 0 Td (K)Tj /T1_2 8.11 Tf 5.86 0 Td (])Tj /T1_4 6.57 Tf 2.24 2.35 Td (d)Tj /T1_3 10.96 Tf 7.53 14.56 Td (j)Tj /T1_4 10.96 Tf 4.68 0 Td (f)Tj /T1_4 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_2 10.96 Tf 3.3 1.64 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (x)Tj /T1_2 10.96 Tf 4.9 0 Td (\))Tj /T1_3 10.96 Tf 4.25 0 Td (j)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 493.1256 302.1616 Tm 2.28 4.53 Td (a)Tj /T1_4 10.96 Tf 1.0003 0 0 1.0003 496.1665 306.6928 Tm 6.28 -4.53 Td [(d)-52(x)]TJ /T1_6 10.96 Tf 10.95 25.31 Td (1)Tj 0 -19.28 TD (C)Tj 0 -7 TD (A)Tj /T1_1 8.11 Tf 9.59 23.58 Td (1)Tj /T1_5 8.11 Tf 4.05 0 Td (=)Tj /T1_8 8.11 Tf 1.0003 0 0.1671 1.0003 527.045 324.7778 Tm 4.05 0 Td (a)Tj /T1_4 10.96 Tf 1.0003 0 0 1.0003 531.0961 324.7778 Tm -218.9 -57.8 Td [(tends)-245(to)-246(0)-246(if)]TJ 54 0 Td (K)Tj 10.6 0 Td [(goes)-246(to)-246(in\002nity)54(.)-245(Let)]TJ /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 376.7537 266.9619 Tm 85.96 0 Td (e)Tj /T1_5 10.96 Tf 1.0003 0 0 1.0003 462.7373 266.9619 Tm 8.12 0 Td (>)Tj /T1_1 10.96 Tf 10.9 0 Td (0)Tj /T1_4 10.96 Tf 5.48 0 Td [(.)-246(If)]TJ /T1_1 10.96 Tf 14.82 0 Td (1)Tj /T1_5 10.96 Tf 7.88 0 Td (<)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 509.9503 266.9619 Tm 10.9 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 520.8532 266.9619 Tm 10.22 0 Td (\267)Tj /T1_1 10.96 Tf 10.91 0 Td (2)Tj /T1_4 10.96 Tf 5.47 0 Td (,)Tj -235.26 -12.3 Td [(c)15(hoose)]TJ 34.48 0 Td (K)Tj /T1_5 10.96 Tf 11.17 0 Td (>)Tj /T1_1 10.96 Tf 11.77 0 Td (0)Tj /T1_4 10.96 Tf 9.7 0 Td [(suc)14(h)-384(that)]TJ 45.42 0 Td [(E)-72(r)-23(r)]TJ /T1_2 10.96 Tf 16.52 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_4 8.11 Tf 6.42 -1.64 Td (K)Tj /T1_2 10.96 Tf 6.35 1.64 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\)\))Tj /T1_3 10.96 Tf 11.76 0 Td (\267)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 501.788 254.6585 Tm 11.77 0 Td (e)Tj /T1_5 10.96 Tf 1.0003 0 0 1.0003 513.5612 254.6585 Tm 5.72 0 Td (=)Tj /T1_1 10.96 Tf 5.48 0 Td (2)Tj /T1_4 10.96 Tf 5.48 0 Td [(.)-386(W)91(e)]TJ -218.05 -12.3 Td [(can)-249(apply)-250(Theor)36(em)-249(1)-250(to)]TJ 106.4 0 Td (X)Tj /T1_4 8.11 Tf 6.42 -1.64 Td (K)Tj /T1_2 10.96 Tf 6.35 1.64 Td (\()Tj /T1_3 10.96 Tf 4.25 0 Td (\242)Tj /T1_2 10.96 Tf 3.04 0 Td (\))Tj /T1_4 10.96 Tf 6.99 0 Td [(suc)15(h)-249(that)]TJ -71.8 -22.06 Td [(E)-72(r)-23(r)]TJ /T1_2 10.96 Tf 16.52 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_4 8.11 Tf 6.42 -1.64 Td (K)Tj /T1_2 10.96 Tf 6.35 1.64 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_1 10.96 Tf 6.84 2.18 Td (\230)Tj /T1_4 10.96 Tf -2.59 -2.18 Td (X)Tj /T1_2 8.11 Tf 7.72 5.8 Td (\()Tj /T1_4 8.11 Tf 3.15 0 Td (n)Tj /T1_2 8.11 Tf 4.05 0 Td (\))Tj /T1_4 8.11 Tf -8.5 -9.04 Td (K)Tj /T1_2 10.96 Tf 12.15 3.24 Td (\()Tj /T1_4 10.96 Tf 3.97 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\)\))Tj /T1_3 10.96 Tf 10.94 0 Td (\267)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 460.9068 220.2891 Tm 10.95 0 Td (e)Tj /T1_5 10.96 Tf 1.0003 0 0 1.0003 471.8598 220.2891 Tm 5.72 0 Td (=)Tj /T1_1 10.96 Tf 5.47 0 Td (2)Tj /T1_4 10.96 Tf -170.87 -18.74 Td (for)Tj 15.52 0 Td (n)Tj /T1_3 10.96 Tf 7.91 0 Td (2)Tj /T1_7 10.96 Tf 9.74 0 Td (N)Tj /T1_4 10.96 Tf 10.65 0 Td [(lar)37(g)10(e)-249(enough.)-250(Then)]TJ -42.42 -21.58 Td [(E)-72(r)-23(r)]TJ /T1_2 10.96 Tf 16.52 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_1 10.96 Tf 6.84 2.18 Td (\230)Tj /T1_4 10.96 Tf -2.58 -2.18 Td (X)Tj /T1_2 8.11 Tf 7.72 5.8 Td (\()Tj /T1_4 8.11 Tf 3.14 0 Td (n)Tj /T1_2 8.11 Tf 4.06 0 Td (\))Tj /T1_4 8.11 Tf -8.5 -9.04 Td (K)Tj /T1_2 10.96 Tf 12.14 3.24 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\)\))Tj /T1_3 10.96 Tf 18.46 0 Td (\267)Tj /T1_4 10.96 Tf 18.47 0 Td [(E)-73(r)-23(r)]TJ /T1_2 10.96 Tf 16.52 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_2 10.96 Tf 7.73 0 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_4 8.11 Tf 6.42 -1.64 Td (K)Tj /T1_2 10.96 Tf 6.35 1.64 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td [(\))1(\))]TJ -31.3 -19.1 Td (+)Tj /T1_4 10.96 Tf 8.51 0 Td [(E)-73(r)-23(r)]TJ /T1_2 10.96 Tf 16.52 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_4 8.11 Tf 6.42 -1.65 Td (K)Tj /T1_2 10.96 Tf 6.36 1.65 Td (\()Tj /T1_4 10.96 Tf 3.97 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_1 10.96 Tf 6.84 2.18 Td (\230)Tj /T1_4 10.96 Tf -2.58 -2.18 Td (X)Tj /T1_2 8.11 Tf 7.72 5.79 Td (\()Tj /T1_4 8.11 Tf 3.14 0 Td (n)Tj /T1_2 8.11 Tf 4.06 0 Td (\))Tj /T1_4 8.11 Tf -8.5 -9.04 Td (K)Tj /T1_2 10.96 Tf 12.14 3.25 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\)\))Tj /T1_3 10.96 Tf -137.14 -20.21 Td (\267)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 403.1209 140.6372 Tm 18.43 7.42 Td (e)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 350.7 -626.34 m 356.42 -626.34 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 350.82 -636.59 Td (2)Tj /T1_2 10.96 Tf 8.32 7.51 Td (+)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 431.2386 140.6372 Tm 9.99 7.42 Td (e)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 370.36 -626.34 m 376.08 -626.34 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 370.48 -636.59 Td (2)Tj /T1_2 10.96 Tf 9.23 7.51 Td (=)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 451.8143 140.6372 Tm 10.95 0 Td (e)Tj /T1_5 10.96 Tf 1.0003 0 0 1.0003 462.7673 140.6372 Tm 5.72 0 Td (:)Tj /T1_4 10.96 Tf -156.31 -22.45 Td (If)Tj /T1_1 10.96 Tf 18.47 0 Td (0)Tj /T1_5 10.96 Tf 12.94 0 Td (<)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 343.5546 118.181 Tm 15.97 0 Td (a)Tj /T1_5 10.96 Tf 1.0003 0 0 1.0003 359.5289 118.181 Tm 15.27 0 Td (<)Tj /T1_1 10.96 Tf 15.97 0 Td (1)Tj /T1_4 10.96 Tf 5.48 0 Td [(,)-1076(c)14(hoose)]TJ 56.57 0 Td (K)Tj /T1_5 10.96 Tf 15.36 0 Td (>)Tj /T1_1 10.96 Tf 15.97 0 Td (0)Tj /T1_4 10.96 Tf 17.26 0 Td [(suc)14(h)-1074(that)]TJ -189.26 -12.3 Td [(E)-72(r)-23(r)]TJ /T1_2 10.96 Tf 16.52 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_4 8.11 Tf 6.42 -1.65 Td (K)Tj /T1_2 10.96 Tf 6.36 1.65 Td (\()Tj /T1_4 10.96 Tf 3.97 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\)\))Tj /T1_3 10.96 Tf 14.51 0 Td (\267)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 391.9679 105.8777 Tm 14.52 0 Td (e)Tj /T1_8 8.11 Tf 5.06 3.97 Td (a)Tj /T1_5 10.96 Tf 1.0003 0 0 1.0003 412.2134 109.8488 Tm 6.28 -3.97 Td (=)Tj /T1_1 10.96 Tf 5.48 0 Td (2)Tj /T1_4 10.96 Tf 5.48 0 Td [(.)-840(Again,)-838(we)-837(can)-837(apply)]TJ -117.29 -12.3 Td [(Theor)37(em)-249(1)-250(to)]TJ 60.76 0 Td (X)Tj /T1_4 8.11 Tf 6.42 -1.65 Td (K)Tj /T1_2 10.96 Tf 6.35 1.65 Td (\()Tj /T1_3 10.96 Tf 4.25 0 Td (\242)Tj /T1_2 10.96 Tf 3.03 0 Td (\))Tj /T1_4 10.96 Tf 6.99 0 Td [(suc)14(h)-249(that)]TJ -29.3 -22.06 Td [(E)-73(r)-23(r)]TJ /T1_2 10.96 Tf 16.52 0 Td (\()Tj /T1_4 10.96 Tf 4.25 0 Td (X)Tj /T1_4 8.11 Tf 6.42 -1.64 Td (K)Tj /T1_2 10.96 Tf 6.36 1.64 Td (\()Tj /T1_4 10.96 Tf 3.97 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_1 10.96 Tf 6.84 2.18 Td (\230)Tj /T1_4 10.96 Tf -2.58 -2.18 Td (X)Tj /T1_2 8.11 Tf 7.72 5.8 Td (\()Tj /T1_4 8.11 Tf 3.15 0 Td (n)Tj /T1_2 8.11 Tf 4.05 0 Td (\))Tj /T1_4 8.11 Tf -8.5 -9.04 Td (K)Tj /T1_2 10.96 Tf 12.14 3.24 Td (\()Tj /T1_4 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\)\))Tj /T1_3 10.96 Tf 10.94 0 Td (\267)Tj /T1_8 10.96 Tf 1.0003 0 0.1671 1.0003 457.7659 71.5082 Tm 10.94 0 Td (e)Tj /T1_8 8.11 Tf 4.97 4.53 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10.96 Tf 4.24 4.19 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 4.53 Td (e)Tj 1.21 -8.72 Td (j)Tj /T1_3 8.11 Tf 2.46 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.35 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.35 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_5 10.96 Tf 4.23 4.19 Td (:)Tj /T1_1 10.96 Tf -225 -49.19 Td [(The)-263(idea)-264(is)-264(no)24(w)-263(to)-264(cut)-264(of)24(f)-263(this)-264(series)-264(at)-264(a)-264(certain)-264(detail)]TJ 0 -12.42 TD [(le)24(v)15(el)]TJ /T1_2 10.96 Tf 24.08 0 Td (k)Tj /T1_6 10.96 Tf 7.75 0 Td (=)Tj /T1_2 10.96 Tf 11.22 0 Td (n)Tj /T1_1 10.96 Tf 5.47 0 Td [(,)-294(that)-294(is)-294(to)-293(approximate)-294(the)-294(k)9(ernel)-293(function)]TJ /T1_2 10.96 Tf -46.88 -12.43 Td (f)Tj /T1_2 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_1 10.96 Tf 6.04 1.64 Td (by)Tj -6.29 -23.05 Td (\230)Tj /T1_2 10.96 Tf -1.32 -2.43 Td (f)Tj /T1_6 8.11 Tf 4.65 5.79 Td (\()Tj /T1_2 8.11 Tf 3.14 0 Td (n)Tj /T1_6 8.11 Tf 4.06 0 Td 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6.57 Tf 4.05 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_5 10.96 Tf 4.23 4.18 Td (:)Tj /T1_1 10.96 Tf -225 -42.96 Td [(The)-255(follo)24(wing)-255(lemma)-255(pro)14(vides)-255(an)-256(upper)-255(bound)-256(for)-256(the)]TJ T* [(approximation)-410(error)-410(of)-410(bounded)-410(k)9(ernel)-409(functions)-410(by)]TJ 0 -12.43 TD [(applying)-250(this)-250(truncation)-250(method.)]TJ 0 -28.36 TD [(Lemma)-250(5)]TJ /T1_2 10.96 Tf 0 -12.43 TD (Let)Tj /T1_1 10.96 Tf 17.64 0 Td (0)Tj /T1_5 10.96 Tf 8.41 0 Td (<)Tj /T1_4 10.96 Tf 1.0003 0 0.1671 1.0003 83.1131 437.7988 Tm 11.45 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 94.5662 437.7988 Tm 10.76 0 Td (\267)Tj /T1_1 10.96 Tf 11.45 0 Td (2)Tj /T1_2 10.96 Tf 5.47 0 Td [(.)-332(If)]TJ /T1_1 10.96 Tf 16.72 0 Td (1)Tj /T1_5 10.96 Tf 8.41 0 Td (<)Tj /T1_4 10.96 Tf 1.0003 0 0.1671 1.0003 147.3907 437.7988 Tm 11.45 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 158.8439 437.7988 Tm 10.76 0 Td (\267)Tj /T1_1 10.96 Tf 11.44 0 Td (2)Tj /T1_2 10.96 Tf 5.48 0 Td [(,)-332(let)-332(additionally)]TJ 77.57 0 Td (d)Tj /T1_5 10.96 Tf 8.99 0 Td (>)Tj /T1_4 10.96 Tf 1.0003 0 0.1671 1.0003 273.1152 437.7988 Tm 11.44 0 Td (a)Tj /T1_2 10.96 Tf 1.0003 0 0 1.0003 284.5584 437.7988 Tm 7.83 0 Td (.)Tj -235.27 -12.42 Td [(Assume)-327(that)]TJ 57.69 0 Td (M)Tj /T1_2 8.11 Tf 8.65 -1.65 Td (t)Tj /T1_1 10.96 Tf 6.21 1.65 Td (:)Tj /T1_6 10.96 Tf 3.04 0 Td (=)Tj /T1_1 10.96 Tf 21.86 0 Td (sup)Tj /T1_2 8.11 Tf -10.44 -11.07 Td (x)Tj /T1_3 8.11 Tf 3.62 0 Td (2)Tj /T1_6 8.11 Tf 5.4 0 Td ([)Tj /T1_3 8.11 Tf 2.25 0 Td (\241)Tj /T1_2 8.11 Tf 6.3 0 Td (A)Tj /T1_5 8.11 Tf 4.95 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (A)Tj /T1_6 8.11 Tf 4.95 0 Td (])Tj /T1_2 6.57 Tf 2.25 2.34 Td (d)Tj /T1_3 10.96 Tf 5.34 8.73 Td (j)Tj /T1_2 10.96 Tf 4.68 0 Td (f)Tj /T1_2 8.11 Tf 3.12 -1.65 Td (t)Tj /T1_6 10.96 Tf 3.3 1.65 Td (\()Tj /T1_2 10.96 Tf 4.25 0 Td (x)Tj /T1_6 10.96 Tf 4.9 0 Td (\))Tj /T1_3 10.96 Tf 4.25 0 Td (j)Tj 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(\241)Tj /T1_1 10.96 Tf 10.03 0 Td (1)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 0 G 0.44 w 10 M 0 j 0 J []0 d 74.67 -396.9 m 114.24 -396.9 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 74.67 -407.19 Td (2)Tj /T1_2 8.11 Tf 5.48 3.17 Td (d)Tj /T1_3 8.11 Tf 4.47 0 Td (\241)Tj /T1_4 8.11 Tf 1.0003 0 0.1671 1.0003 156.6432 365.759 Tm 6.3 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 162.945 365.759 Tm 7.81 -3.17 Td (\241)Tj /T1_1 10.96 Tf 10.04 0 Td (1)Tj /T1_8 10.96 Tf 6.67 23 Td (\266)Tj /T1_1 8.11 Tf 8.06 -1.61 Td (1)Tj /T1_5 8.11 Tf 4.06 0 Td (=)Tj /T1_4 8.11 Tf 1.0003 0 0.1671 1.0003 199.595 383.984 Tm 4.05 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 203.6461 383.984 Tm 7.81 -13.84 Td (\242)Tj /T1_2 10.96 Tf 4.55 0 Td (d)Tj /T1_1 8.11 Tf 6.05 4.52 Td (1)Tj /T1_5 8.11 Tf 4.06 0 Td (=)Tj /T1_4 8.11 Tf 1.0003 0 0.1671 1.0003 226.1223 374.6615 Tm 4.05 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 230.1734 374.6615 Tm -90.95 -35.18 Td (\242)Tj /T1_2 10.96 Tf 3.04 0 Td (M)Tj /T1_2 8.11 Tf 8.65 -1.65 Td (t)Tj /T1_3 10.96 Tf 4.82 1.65 Td (\242)Tj /T1_6 10.96 Tf 4.56 0 Td (\()Tj /T1_1 10.96 Tf 4.25 0 Td (2)Tj /T1_2 10.96 Tf 5.48 0 Td (A)Tj /T1_6 10.96 Tf 6.69 0 Td (\))Tj /T1_2 8.11 Tf 4.25 4.52 Td (d)Tj /T1_5 8.11 Tf 4.48 0 Td (=)Tj /T1_4 8.11 Tf 1.0003 0 0.1671 1.0003 185.4311 343.9931 Tm 4.05 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 189.4823 343.9931 Tm 7.81 -4.52 Td (\242)Tj /T1_8 10.96 Tf 4.56 15.45 Td (\265)Tj /T1_1 10.96 Tf 21.84 -8.04 Td (1)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 139.08 -427.56 m 169.72 -427.56 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 139.08 -438.34 Td (2)Tj /T1_2 8.11 Tf 5.47 3.21 Td (d)Tj /T1_5 8.11 Tf 4.48 0 Td (=)Tj /T1_4 8.11 Tf 1.0003 0 0.1671 1.0003 221.0709 334.6405 Tm 4.05 0 Td (a)Tj /T1_3 8.11 Tf 1.0003 0 0 1.0003 225.122 334.6405 Tm 5.79 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (1)Tj /T1_8 10.96 Tf 5.75 20.28 Td (\266)Tj /T1_2 8.11 Tf 8.06 -2.7 Td (n)Tj /T1_2 10.96 Tf -193.92 -41.89 Td (if)Tj /T1_1 10.96 Tf 8.83 0 Td (0)Tj /T1_5 10.96 Tf 7.91 0 Td (<)Tj /T1_4 10.96 Tf 1.0003 0 0.1671 1.0003 73.8005 310.3238 Tm 10.95 0 Td (a)Tj /T1_5 10.96 Tf 1.0003 0 0 1.0003 84.7535 310.3238 Tm 10.26 0 Td (<)Tj /T1_1 10.96 Tf 10.94 0 Td (1)Tj /T1_2 10.96 Tf 8.22 0 Td (and)Tj /T1_3 10.96 Tf -51.5 -30.48 Td (k)Tj /T1_2 10.96 Tf 7.12 0 Td (f)Tj /T1_2 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_3 10.96 Tf 4.82 1.64 Td (\241)Tj /T1_1 10.96 Tf 13 2.44 Td (\230)Tj /T1_2 10.96 Tf -1.32 -2.44 Td (f)Tj /T1_6 8.11 Tf 4.65 5.8 Td (\()Tj /T1_2 8.11 Tf 3.14 0 Td (n)Tj /T1_6 8.11 Tf 4.06 0 Td (\))Tj /T1_2 8.11 Tf -8.73 -8.18 Td (t)Tj /T1_5 8.11 Tf 2.8 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td [(cu)25(t)]TJ /T1_3 10.96 Tf 10.75 2.38 Td (k)Tj /T1_2 8.11 Tf 5.48 -1.81 Td (L)Tj /T1_4 6.57 Tf 1.0003 0 0.1671 1.0003 113.8215 278.0249 Tm 4.14 2.34 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 118.3527 280.3656 Tm 8.12 -0.53 Td (\267)Tj /T1_1 10.96 Tf 22.24 7.42 Td (2)Tj /T1_2 8.11 Tf 5.48 3.98 Td (d)Tj /T1_3 10.96 Tf 6.5 -3.98 Td (\241)Tj /T1_1 10.96 Tf 10.03 0 Td (1)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 66.61 -487.18 m 114.29 -487.18 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 66.61 -497.95 Td (2)Tj /T1_2 8.11 Tf 5.48 3.2 Td (d)Tj /T1_5 8.11 Tf 4.47 0 Td (=)Tj /T1_4 8.11 Tf 1.0003 0 0.1671 1.0003 148.581 275.0041 Tm 4.05 0 Td (a)Tj /T1_3 8.11 Tf 1.0003 0 0 1.0003 152.6321 275.0041 Tm 5.79 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (1)Tj /T1_3 10.96 Tf 6.08 -3.2 Td (\241)Tj /T1_1 10.96 Tf 10.03 0 Td (1)Tj /T1_3 10.96 Tf 8.2 8.03 Td (\242)Tj /T1_2 10.96 Tf 4.55 0 Td (d)Tj /T1_3 10.96 Tf -54.38 -29.2 Td (\242)Tj /T1_2 10.96 Tf 3.04 0 Td (M)Tj /T1_2 8.11 Tf 8.65 -1.64 Td (t)Tj /T1_3 10.96 Tf 4.82 1.64 Td (\242)Tj /T1_6 10.96 Tf 4.56 0 Td (\()Tj /T1_1 10.96 Tf 4.25 0 Td (2)Tj /T1_2 10.96 Tf 5.48 0 Td (A)Tj /T1_6 10.96 Tf 6.69 0 Td (\))Tj /T1_2 8.11 Tf 4.25 4.53 Td (d)Tj /T1_5 8.11 Tf 4.48 0 Td (=)Tj /T1_4 8.11 Tf 1.0003 0 0.1671 1.0003 185.4311 255.1587 Tm 4.05 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 189.4823 255.1587 Tm 7.81 -4.53 Td (\242)Tj /T1_8 10.96 Tf 4.56 15.46 Td (\265)Tj /T1_1 10.96 Tf 21.84 -8.04 Td (1)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 139.08 -516.38 m 169.72 -516.38 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 139.08 -527.15 Td (2)Tj /T1_2 8.11 Tf 5.47 3.2 Td (d)Tj /T1_5 8.11 Tf 4.48 0 Td (=)Tj /T1_4 8.11 Tf 1.0003 0 0.1671 1.0003 221.0709 245.7961 Tm 4.05 0 Td (a)Tj /T1_3 8.11 Tf 1.0003 0 0 1.0003 225.122 245.7961 Tm 5.79 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (1)Tj /T1_8 10.96 Tf 5.75 20.29 Td (\266)Tj /T1_2 8.11 Tf 8.06 -2.71 Td (n)Tj /T1_2 10.96 Tf -193.92 -41.89 Td (if)Tj /T1_1 10.96 Tf 8.83 0 Td (1)Tj /T1_3 10.96 Tf 7.91 0 Td (\267)Tj /T1_4 10.96 Tf 1.0003 0 0.1671 1.0003 73.8005 221.4794 Tm 10.95 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 84.7535 221.4794 Tm 10.26 0 Td (\267)Tj /T1_1 10.96 Tf 10.94 0 Td (2)Tj /T1_2 10.96 Tf 5.48 0 Td (.)Tj /T1_1 10.96 Tf -54.37 -28.36 Td [(Remark)-250(6)]TJ /T1_2 10.96 Tf 0 -12.42 TD (When)Tj 33.16 0 Td (f)Tj /T1_2 8.11 Tf 3.12 -1.65 Td (t)Tj /T1_2 10.96 Tf 3.3 1.65 Td (,)Tj 9.04 0 Td (t)Tj /T1_3 10.96 Tf 8.35 0 Td (2)Tj /T1_6 10.96 Tf 11.86 0 Td ([)Tj /T1_3 10.96 Tf 3.03 0 Td (\241)Tj /T1_2 10.96 Tf 8.52 0 Td (T)Tj /T1_5 10.96 Tf 6.67 0 Td (;)Tj /T1_2 10.96 Tf 4.25 0 Td (T)Tj /T1_6 10.96 Tf 7.48 0 Td (])Tj /T1_2 8.11 Tf 3.04 3.97 Td (d)Tj /T1_2 10.96 Tf 11.54 -3.97 Td [(is)-599(assumed)-600(to)-599(be)-600(H)]TJ 98.98 -0.08 Td (\250)Tj -0.89 0.08 Td [(older)20(-)]TJ -211.45 -12.43 Td [(continuous)-238(on)]TJ /T1_6 10.96 Tf 64.26 0 Td ([)Tj /T1_3 10.96 Tf 3.03 0 Td (\241)Tj /T1_2 10.96 Tf 8.52 0 Td (A)Tj /T1_5 10.96 Tf 6.69 0 Td (;)Tj /T1_2 10.96 Tf 4.25 0 Td (A)Tj /T1_6 10.96 Tf 6.7 0 Td (])Tj /T1_2 8.11 Tf 3.03 3.98 Td (d)Tj /T1_2 10.96 Tf 4.97 -3.98 Td [(,)-238(the)-238(r)14(ate)-237(of)-239(con)39(ver)37(g)10(ence)-237(of)-238(this)]TJ -101.45 -12.43 Td [(estimate)-250(can)-250(be)-250(impr)44(o)10(ved,)-249(see)-250(Kar)36(c)15(her)-249(et)-250(al.)-250(\(2009\).)]TJ /T1_1 10.96 Tf 0 -34.58 TD [(T)79(aking)-427(a)-428(w)9(a)20(v)15(elet)-427(basis)-429(for)]TJ /T1_2 10.96 Tf 126.75 0 Td (L)Tj /T1_1 8.11 Tf 6.13 3.97 Td (max)Tj /T1_3 8.11 Tf 13.96 0 Td (f)Tj /T1_4 8.11 Tf 1.0003 0 0.1671 1.0003 203.9362 125.203 Tm 4.05 0 Td (a)Tj /T1_5 8.11 Tf 1.0003 0 0 1.0003 207.9873 125.203 Tm 5.79 0 Td (;)Tj /T1_2 8.11 Tf 2.85 0 Td (p)Tj /T1_3 8.11 Tf 4.06 0 Td (g)Tj /T1_6 10.96 Tf 4.55 -3.97 Td [(\()1([)]TJ /T1_3 10.96 Tf 7.28 0 Td (\241)Tj /T1_2 10.96 Tf 8.52 0 Td (A)Tj /T1_5 10.96 Tf 6.69 0 Td (;)Tj /T1_2 10.96 Tf 4.25 0 Td (A)Tj /T1_6 10.96 Tf 6.7 0 Td (])Tj /T1_2 8.11 Tf 3.03 3.97 Td (d)Tj /T1_6 10.96 Tf 4.97 -3.97 Td (\))Tj /T1_1 10.96 Tf 8.95 0 Td (with)Tj -218.53 -12.43 Td (1)Tj /T1_5 10.96 Tf 10.76 0 Td (<)Tj /T1_2 10.96 Tf 14.61 0 Td (p)Tj /T1_3 10.96 Tf 10.76 0 Td (\267)Tj /T1_1 10.96 Tf 13.8 0 Td (2)Tj 13.34 0 Td [(has)-717(adv)24(antages)-717(in)-717(particular)-718(in)-718(the)]TJ -63.27 -12.43 Td [(representation)-489(of)-490(functions)-489(with)-490(discontinuities)-490(and)]TJ 0 -12.42 TD [(sharp)-531(peaks,)-533(that)-531(is)-532(functions)-532(with)-532(a)-532(certain)-532(local)]TJ 0 -12.43 TD [(beha)19(vior)55(.)-555(By)-555(simply)-555(cutting)-555(of)-554(at)-555(a)-555(certain)-555(detail)]TJ 255.01 676.28 Td [(le)25(v)15(el,)-530(this)-530(adv)24(antage)-529(is)-530(not)-530(honored.)-532(In)-530(this)-530(vie)24(w)65(,)]TJ 0 -12.45 TD [(it)-583(is)-583(better)-584(to)-583(approximate)-583(the)-584(k)9(ernel)-582(function)]TJ /T1_2 10.96 Tf 231.58 0 Td (f)Tj /T1_2 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_1 10.96 Tf -234.7 -13.61 Td [(with)-381(a)-382(truncated)-381(Haar)-382(series)]TJ 135.21 2.44 Td (\230)Tj /T1_2 10.96 Tf -1.32 -2.44 Td (f)Tj /T1_6 8.11 Tf 4.65 5.8 Td (\()Tj /T1_2 8.11 Tf 3.15 0 Td (n)Tj /T1_6 8.11 Tf 4.05 0 Td (\))Tj /T1_2 8.11 Tf -8.73 -8.18 Td (t)Tj /T1_1 10.96 Tf 16.55 2.38 Td [(that)-382(contains)-381(those)]TJ /T1_2 10.96 Tf -153.56 -12.45 Td (n)Tj /T1_1 10.96 Tf 11.91 0 Td (summands)Tj /T1_6 10.96 Tf 53.3 0 Td (\()Tj /T1_2 10.96 Tf 5.89 0 Td (f)Tj /T1_5 10.96 Tf 4.54 0 Td (;)Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 3.98 Td (e)Tj 1.22 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.45 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.06 2.34 Td (k)Tj /T1_2 8.11 Tf 3.52 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_6 10.96 Tf 4.24 4.73 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 3.98 Td (e)Tj 1.21 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.46 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_1 10.96 Tf 10.66 4.73 Td [(with)-587(the)-587(lar)17(gest)]TJ -163.26 -15.64 Td [(v)25(alues)]TJ /T1_3 10.96 Tf 31.82 0 Td (k)Tj /T1_6 10.96 Tf 5.47 0 Td (\()Tj /T1_2 10.96 Tf 5.9 0 Td (f)Tj /T1_5 10.96 Tf 4.53 0 Td (;)Tj /T1_7 10.96 Tf 4.26 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 3.98 Td (e)Tj 1.21 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.46 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.24 0 Td (k)Tj /T1_6 10.96 Tf 4.24 4.73 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 3.98 Td (e)Tj 1.22 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.45 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.06 2.34 Td (k)Tj /T1_2 8.11 Tf 3.52 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_3 10.96 Tf 4.24 4.73 Td (k)Tj /T1_2 8.11 Tf 5.47 -1.81 Td (L)Tj /T1_4 6.57 Tf 1.0003 0 0.1671 1.0003 446.5629 690.3582 Tm 4.14 2.34 Td (a)Tj /T1_1 10.96 Tf 1.0003 0 0 1.0003 451.0941 692.6988 Tm 9.79 -0.53 Td (and)Tj /T1_3 10.96 Tf 19.92 0 Td (k)Tj /T1_6 10.96 Tf 5.48 0 Td (\()Tj /T1_2 10.96 Tf 5.89 0 Td (f)Tj /T1_5 10.96 Tf 4.54 0 Td (;)Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_3 8.11 Tf 8.71 3.98 Td (\244)Tj /T1_6 10.96 Tf 4.55 -3.98 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_3 8.11 Tf 8.71 3.98 Td (\244)Tj /T1_3 10.96 Tf 4.56 -3.98 Td (k)Tj /T1_2 8.11 Tf 5.47 -1.81 Td (L)Tj /T1_4 6.57 Tf 1.0003 0 0.1671 1.0003 537.2377 690.3582 Tm 4.14 2.34 Td (a)Tj /T1_1 10.96 Tf 1.0003 0 0 1.0003 541.769 692.6988 Tm 5.69 -0.53 Td (,)Tj -235.26 -14.92 Td [(see)-335(Karcher)]TJ /T1_2 10.96 Tf 56.61 0 Td [(et)-335(al.)]TJ /T1_1 10.96 Tf 26.53 0 Td [(\(2009\).)-335(In)-335(this)-336(paper)39(,)-334(an)-336(algorithm)]TJ -83.14 -12.45 Td [(is)-341(presented)-342(which)-343(determines)-342(an)-342(approximation)]TJ 223.83 2.43 Td (\230)Tj /T1_2 10.96 Tf -1.32 -2.43 Td (f)Tj /T1_6 8.11 Tf 4.65 3.98 Td (\()Tj /T1_2 8.11 Tf 3.15 0 Td (n)Tj /T1_6 8.11 Tf 4.05 0 Td (\))Tj /T1_1 10.96 Tf -234.36 -16.43 Td [(close)-249(to)-250(this)-250(particular)-250(truncation.)]TJ 0 -18.67 TD [(W)80(e)-239(denote)-239(by)]TJ /T1_2 10.96 Tf 62.36 0 Td (I)Tj /T1_1 10.96 Tf 6.84 0 Td [(the)-239(set)-239(of)-240(the)-239(indices)]TJ /T1_6 10.96 Tf 92.23 0 Td (\()Tj /T1_2 10.96 Tf 4.25 0 Td (e)Tj /T1_5 10.96 Tf 4.76 0 Td (;)Tj /T1_2 10.96 Tf 5.89 0 Td (j)Tj /T1_5 10.96 Tf 3.32 0 Td (;)Tj /T1_2 10.96 Tf 4.25 0 Td (k)Tj /T1_6 10.96 Tf 5.05 0 Td (\))Tj /T1_1 10.96 Tf 6.88 0 Td [(for)-239(which)]TJ -195.83 -12.45 Td [(the)-476(summands)]TJ /T1_6 10.96 Tf 70.69 0 Td (\()Tj /T1_2 10.96 Tf 5.9 0 Td (f)Tj /T1_2 8.11 Tf 3.11 -1.65 Td (t)Tj /T1_5 10.96 Tf 3.31 1.65 Td (;)Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 3.97 Td (e)Tj 1.21 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.46 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.35 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.35 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_6 10.96 Tf 4.23 4.74 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 3.97 Td (e)Tj 1.22 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.46 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.35 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.35 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.24 0 Td (k)Tj /T1_1 10.96 Tf 9.46 4.74 Td [(are)-476(part)-476(of)-476(the)]TJ -169.42 -19.3 Td [(truncated)-249(w)9(a)20(v)15(elet)-249(series)]TJ 110.47 2.43 Td (\230)Tj /T1_2 10.96 Tf -1.32 -2.43 Td (f)Tj /T1_6 8.11 Tf 4.64 5.79 Td (\()Tj /T1_2 8.11 Tf 3.15 0 Td (n)Tj /T1_6 8.11 Tf 4.05 0 Td (\))Tj /T1_2 8.11 Tf -8.72 -8.18 Td (t)Tj /T1_1 10.96 Tf 12.37 2.39 Td [(.)-249(Then)-250(we)-250(can)-250(write)]TJ -109.25 -23.87 Td (\230)Tj /T1_2 10.96 Tf -1.32 -2.43 Td (f)Tj /T1_6 8.11 Tf 4.65 5.79 Td (\()Tj /T1_2 8.11 Tf 3.15 0 Td (n)Tj /T1_6 8.11 Tf 4.05 0 Td (\))Tj /T1_2 8.11 Tf -8.73 -8.17 Td (t)Tj /T1_6 10.96 Tf 14.81 2.38 Td [(=)-221(\()]TJ /T1_2 10.96 Tf 16.84 0 Td (f)Tj /T1_2 8.11 Tf 3.12 -1.65 Td (t)Tj /T1_5 10.96 Tf 3.3 1.65 Td (;)Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_3 8.11 Tf 8.71 4.52 Td (\244)Tj /T1_6 10.96 Tf 4.55 -4.52 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_3 8.11 Tf 8.71 4.52 Td (\244)Tj /T1_6 10.96 Tf 6.08 -4.52 Td (+)Tj /T1_7 15.78 Tf 19.52 -2.34 Td (\345)Tj /T1_6 8.11 Tf -9.49 -9.61 Td (\()Tj /T1_2 8.11 Tf 3.15 0 Td (e)Tj /T1_5 8.11 Tf 3.51 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_5 8.11 Tf 3.74 0 Td (;)Tj /T1_2 8.11 Tf 3.46 0 Td (j)Tj /T1_6 8.11 Tf 2.46 0 Td (\))Tj /T1_3 8.11 Tf 3.14 0 Td (2)Tj /T1_2 8.11 Tf 5.4 0 Td (I)Tj /T1_6 10.96 Tf 3.11 11.95 Td (\()Tj /T1_2 10.96 Tf 5.9 0 Td (f)Tj /T1_2 8.11 Tf 3.11 -1.65 Td (t)Tj /T1_5 10.96 Tf 3.31 1.65 Td (;)Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 4.52 Td (e)Tj 1.22 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.45 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_6 10.96 Tf 4.23 4.19 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 4.52 Td (e)Tj 1.22 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.46 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.24 0 Td (k)Tj /T1_1 10.96 Tf -221.33 -31.05 Td (if)Tj /T1_6 10.96 Tf 9.43 0 Td (\()Tj /T1_2 10.96 Tf 5.89 0 Td (f)Tj /T1_2 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_5 10.96 Tf 3.3 1.64 Td (;)Tj /T1_7 10.96 Tf 4.26 0 Td (Y)Tj /T1_3 8.11 Tf 8.71 3.98 Td (\244)Tj /T1_6 10.96 Tf 4.55 -3.98 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_3 8.11 Tf 8.71 3.98 Td (\244)Tj /T1_1 10.96 Tf 7.29 -3.98 Td [(is)-249(included)-250(in)-250(the)-250(truncated)-250(series)-250(or)]TJ -14.67 -24.14 Td (\230)Tj /T1_2 10.96 Tf -1.32 -2.43 Td (f)Tj /T1_6 8.11 Tf 4.65 5.8 Td (\()Tj /T1_2 8.11 Tf 3.14 0 Td (n)Tj /T1_6 8.11 Tf 4.06 0 Td (\))Tj /T1_2 8.11 Tf -8.73 -8.18 Td (t)Tj /T1_6 10.96 Tf 14.8 2.38 Td (=)Tj /T1_7 15.78 Tf 20.44 -2.34 Td (\345)Tj /T1_6 8.11 Tf -9.49 -9.61 Td (\()Tj /T1_2 8.11 Tf 3.15 0 Td (e)Tj /T1_5 8.11 Tf 3.52 0 Td (;)Tj /T1_2 8.11 Tf 2.24 0 Td (k)Tj /T1_5 8.11 Tf 3.74 0 Td (;)Tj /T1_2 8.11 Tf 3.46 0 Td (j)Tj /T1_6 8.11 Tf 2.46 0 Td (\))Tj /T1_3 8.11 Tf 3.14 0 Td (2)Tj /T1_2 8.11 Tf 5.4 0 Td (I)Tj /T1_6 10.96 Tf 3.12 11.95 Td (\()Tj /T1_2 10.96 Tf 5.89 0 Td (f)Tj /T1_2 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_5 10.96 Tf 3.3 1.64 Td (;)Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 4.53 Td (e)Tj 1.22 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.45 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.06 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.59 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_6 10.96 Tf 4.24 4.18 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 4.53 Td (e)Tj 1.21 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.46 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_1 10.96 Tf -191.89 -30.31 Td [(if)-249(it)-250(is)-250(not)-250(included.)]TJ 0 -18.68 TD [(In)-249(order)-250(to)-250(approximate)-250(the)-250(random)-250(\002eld)]TJ /T1_2 10.96 Tf 181.04 0 Td (X)Tj /T1_1 10.96 Tf 7.73 0 Td [(,)-249(we)-250(use)]TJ -183.07 -29.12 Td (\230)Tj /T1_2 10.96 Tf -2.58 -2.18 Td (X)Tj /T1_6 8.11 Tf 7.72 4.53 Td (\()Tj /T1_2 8.11 Tf 3.15 0 Td (n)Tj /T1_6 8.11 Tf 4.05 0 Td (\))Tj /T1_6 10.96 Tf 3.64 -4.53 Td (\()Tj /T1_2 10.96 Tf 3.98 0 Td (t)Tj /T1_6 10.96 Tf 3.79 0 Td [(\))-221(=)-221(\()]TJ /T1_2 10.96 Tf 23.53 0 Td (f)Tj /T1_2 8.11 Tf 3.11 -1.64 Td (t)Tj /T1_5 10.96 Tf 3.31 1.64 Td (;)Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_3 8.11 Tf 8.71 4.53 Td (\244)Tj /T1_6 10.96 Tf 4.55 -4.53 Td (\))Tj /T1_3 10.96 Tf 5.77 0 Td (\242)Tj /T1_2 10.96 Tf 5.75 7.42 Td (M)Tj /T1_6 10.96 Tf 9.57 0 Td [(\()1([)]TJ /T1_3 10.96 Tf 7.28 0 Td (\241)Tj /T1_2 10.96 Tf 8.52 0 Td (A)Tj /T1_5 10.96 Tf 6.69 0 Td (;)Tj /T1_2 10.96 Tf 4.25 0 Td (A)Tj /T1_6 10.96 Tf 6.7 0 Td (])Tj /T1_2 8.11 Tf 3.03 3.98 Td (d)Tj /T1_6 10.96 Tf 4.97 -3.98 Td (\))Tj ET 1.0003 0 0 1.0003 72 769.89 cm 328.51 -337.78 m 383.77 -337.78 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_6 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 339.26 -348.55 Td (\()Tj /T1_1 10.96 Tf 4.25 0 Td (2)Tj /T1_2 10.96 Tf 5.48 0 Td (A)Tj /T1_6 10.96 Tf 6.69 0 Td (\))Tj /T1_2 8.11 Tf 4.25 3.2 Td (d)Tj /T1_5 8.11 Tf 4.48 0 Td (=)Tj /T1_1 8.11 Tf 4.05 0 Td (2)Tj /T1_6 10.96 Tf -88.43 -23.61 Td (+)Tj /T1_7 15.78 Tf 19.22 -2.34 Td (\345)Tj /T1_6 8.11 Tf -9.49 -9.61 Td (\()Tj /T1_2 8.11 Tf 3.14 0 Td (e)Tj /T1_5 8.11 Tf 3.52 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_5 8.11 Tf 3.74 0 Td (;)Tj /T1_2 8.11 Tf 3.46 0 Td (j)Tj /T1_6 8.11 Tf 2.45 0 Td (\))Tj /T1_3 8.11 Tf 3.15 0 Td (2)Tj /T1_2 8.11 Tf 5.4 0 Td (I)Tj /T1_6 10.96 Tf 3.11 11.95 Td (\()Tj /T1_2 10.96 Tf 5.9 0 Td (f)Tj /T1_2 8.11 Tf 3.11 -1.65 Td (t)Tj /T1_5 10.96 Tf 3.31 1.65 Td (;)Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 4.52 Td (e)Tj 1.21 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.46 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_6 10.96 Tf 4.23 4.19 Td (\))Tj /T1_8 9.86 Tf 14.09 13.69 Td (Z)Tj /T1_6 8.11 Tf -10.81 -30.6 Td ([)Tj /T1_3 8.11 Tf 2.25 0 Td (\241)Tj /T1_2 8.11 Tf 6.3 0 Td (A)Tj /T1_5 8.11 Tf 4.95 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (A)Tj /T1_6 8.11 Tf 4.95 0 Td (])Tj /T1_2 6.57 Tf 2.25 2.34 Td (d)Tj /T1_7 10.96 Tf 7.53 14.57 Td (Y)Tj /T1_2 8.11 Tf 8.71 4.52 Td (e)Tj 1.21 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.46 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_2 10.96 Tf 4.23 4.19 Td (M)Tj /T1_6 10.96 Tf 9.57 0 Td (\()Tj /T1_2 10.96 Tf 4.25 0 Td [(d)-51(x)]TJ /T1_6 10.96 Tf 10.94 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (;)Tj /T1_1 10.96 Tf -231.93 -36.97 Td (or)Tj 8.48 -23.59 Td (\230)Tj /T1_2 10.96 Tf -2.58 -2.18 Td (X)Tj /T1_6 8.11 Tf 7.72 4.53 Td (\()Tj /T1_2 8.11 Tf 3.15 0 Td (n)Tj /T1_6 8.11 Tf 4.05 0 Td (\))Tj /T1_6 10.96 Tf 3.64 -4.53 Td (\()Tj /T1_2 10.96 Tf 3.98 0 Td (t)Tj /T1_6 10.96 Tf 3.79 0 Td [(\))-221(=)]TJ /T1_7 15.78 Tf 27.12 -2.34 Td (\345)Tj /T1_6 8.11 Tf -9.49 -9.61 Td (\()Tj /T1_2 8.11 Tf 3.15 0 Td (e)Tj /T1_5 8.11 Tf 3.52 0 Td (;)Tj /T1_2 8.11 Tf 2.24 0 Td (k)Tj /T1_5 8.11 Tf 3.74 0 Td (;)Tj /T1_2 8.11 Tf 3.46 0 Td (j)Tj /T1_6 8.11 Tf 2.46 0 Td (\))Tj /T1_3 8.11 Tf 3.14 0 Td (2)Tj /T1_2 8.11 Tf 5.4 0 Td (I)Tj /T1_6 10.96 Tf 3.12 11.95 Td (\()Tj /T1_2 10.96 Tf 5.89 0 Td (f)Tj /T1_2 8.11 Tf 3.12 -1.64 Td (t)Tj /T1_5 10.96 Tf 3.3 1.64 Td (;)Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 4.53 Td (e)Tj 1.22 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.45 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.06 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.24 0 Td (k)Tj /T1_6 10.96 Tf 4.24 4.18 Td (\))Tj /T1_8 9.86 Tf 14.08 13.69 Td (Z)Tj /T1_6 8.11 Tf -10.8 -30.6 Td ([)Tj /T1_3 8.11 Tf 2.24 0 Td (\241)Tj /T1_2 8.11 Tf 6.3 0 Td (A)Tj /T1_5 8.11 Tf 4.96 0 Td (;)Tj /T1_2 8.11 Tf 2.24 0 Td (A)Tj /T1_6 8.11 Tf 4.96 0 Td (])Tj /T1_2 6.57 Tf 2.24 2.34 Td (d)Tj /T1_7 10.96 Tf 7.53 14.57 Td (Y)Tj /T1_2 8.11 Tf 8.71 4.53 Td (e)Tj 1.22 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.45 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.06 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.24 0 Td (k)Tj /T1_2 10.96 Tf 4.24 4.18 Td (M)Tj /T1_6 10.96 Tf 9.56 0 Td (\()Tj /T1_2 10.96 Tf 4.25 0 Td [(d)-52(x)]TJ /T1_6 10.96 Tf 10.95 0 Td (\))Tj /T1_1 10.96 Tf -227.86 -40.2 Td [(if,)-377(ag)4(ain,)]TJ /T1_6 10.96 Tf 44.12 0 Td (\()Tj /T1_2 10.96 Tf 5.9 0 Td (f)Tj /T1_2 8.11 Tf 3.11 -1.64 Td (t)Tj /T1_5 10.96 Tf 3.31 1.64 Td (;)Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_3 8.11 Tf 8.71 3.98 Td (\244)Tj /T1_6 10.96 Tf 4.55 -3.98 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (Y)Tj /T1_3 8.11 Tf 8.71 3.98 Td (\244)Tj /T1_1 10.96 Tf 8.69 -3.98 Td [(is)-377(not)-378(included)-377(in)-378(the)-378(truncated)]TJ -95.6 -12.45 Td (series.)Tj 0 -18.67 TD [(Since)-580(the)-581(Haar)-581(w)9(a)20(v)15(elets)]TJ /T1_7 10.96 Tf 122.32 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 3.97 Td (e)Tj 1.22 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.45 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_1 10.96 Tf 10.6 4.74 Td [(are)-580(simple)-581(step)]TJ -165.03 -14.9 Td [(functions,)-249(the)-250(inte)14(grals)]TJ /T1_8 9.86 Tf 80.8 -14.32 Td (Z)Tj /T1_6 8.11 Tf -10.81 -30.6 Td ([)Tj /T1_3 8.11 Tf 2.25 0 Td (\241)Tj /T1_2 8.11 Tf 6.3 0 Td (A)Tj /T1_5 8.11 Tf 4.95 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (A)Tj /T1_6 8.11 Tf 4.95 0 Td (])Tj /T1_2 6.57 Tf 2.25 2.34 Td (d)Tj /T1_7 10.96 Tf 7.53 14.57 Td (Y)Tj /T1_2 8.11 Tf 8.71 4.52 Td (e)Tj 1.21 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.46 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_2 10.96 Tf 4.23 4.19 Td (M)Tj /T1_6 10.96 Tf 9.57 0 Td (\()Tj /T1_2 10.96 Tf 4.25 0 Td [(d)-51(x)]TJ /T1_6 10.96 Tf 10.94 0 Td (\))Tj /T1_1 10.96 Tf -161.57 -39.46 Td [(can)-793(be)-795(easily)-794(computed.)-797(Ho)24(we)25(v)15(er)40(,)-794(the)-794(w)9(a)20(v)15(elet)]TJ 0 -12.45 TD [(coef)25(\002cients)]TJ /T1_6 10.96 Tf 53.54 0 Td (\()Tj /T1_2 10.96 Tf 5.9 0 Td (f)Tj /T1_2 8.11 Tf 3.11 -1.64 Td (t)Tj /T1_5 10.96 Tf 3.3 1.64 Td (;)Tj /T1_7 10.96 Tf 4.26 0 Td (Y)Tj /T1_2 8.11 Tf 8.71 3.98 Td (e)Tj 1.21 -8.71 Td (j)Tj /T1_3 8.11 Tf 2.46 0 Td (\241)Tj /T1_1 8.11 Tf 6.3 0 Td (2)Tj /T1_2 6.57 Tf 4.05 2.34 Td (k)Tj /T1_2 8.11 Tf 3.53 -2.34 Td (c)Tj /T1_5 8.11 Tf 3.6 0 Td (;)Tj /T1_2 8.11 Tf 2.25 0 Td (k)Tj /T1_6 10.96 Tf 4.23 4.73 Td (\))Tj /T1_1 10.96 Tf 7.56 0 Td [(cause)-302(problems)-302(if)-302(no)-302(closed)]TJ -114.01 -14.89 Td [(formula)-557(of)-558(the)-557(inte)14(gral)-557(of)-558(the)-557(k)9(ernel)-557(functions)]TJ /T1_2 10.96 Tf 231.58 0 Td (f)Tj /T1_2 8.11 Tf 3.12 -1.65 Td (t)Tj /T1_1 10.96 Tf -234.7 -10.8 Td [(o)15(v)15(er)-455(cubes)-455(is)-456(kno)24(wn.)-455(In)-455(this)-456(case,)-455(the)14(y)-455(ha)19(v)15(e)-454(to)-456(be)]TJ T* [(determined)-593(numerically)-593(by)-594(using)-593(the)-593(f)9(ast)-593(w)9(a)20(v)15(elet)]TJ T* [(transform)-249(\(see)-250(Urban)-250(\(2008\)\).)]TJ 0 -18.68 TD [(The)-204(follo)24(wing)-204(algorithm)-205(can)-206(be)-205(used)-205(for)-205(the)-205(simulation)]TJ 0 -12.45 TD [(of)-249(the)-250(considered)]TJ /T1_4 10.96 Tf 1.0003 0 0.1671 1.0003 312.1359 88.4929 Tm 78.19 0 Td (a)Tj /T1_1 10.96 Tf 1.0003 0 0 1.0003 390.3474 88.4929 Tm 7.82 0 Td [(-stable)-250(random)-250(\002elds.)]TJ -97.25 -51.84 Td (5)Tj ET endstream endobj 126 0 obj 32244 endobj 127 0 obj << /Length 128 0 R >> stream 0 g 1 i /RelativeColorimetric ri BT /T1_0 13.94 Tf 1.0003 0 0 1.0003 72 769.89 Tm -14.94 -21.91 Td [(SIMULA)119(TION)-277(STUD)89(Y)]TJ /T1_1 10.96 Tf 0 -24.51 TD [(F)14(or)-315(the)-317(simulation)-317(study)64(,)-316(we)-317(used)-317(tw)9(o)-316(dif)24(ferent)-316(types)]TJ 0 -12.42 TD [(of)-582(k)9(ernel)-582(functions)-583(for)]TJ /T1_2 10.96 Tf 1.0003 0 0.1671 1.0003 57.0559 711.0338 Tm 115.49 0 Td (a)Tj /T1_1 10.96 Tf 1.0003 0 0 1.0003 172.5776 711.0338 Tm 7.82 0 Td [(-stable)-582(random)-583(\002elds)-582(of)]TJ -123.31 -12.43 Td (dimension)Tj /T1_3 10.96 Tf 49.86 0 Td (d)Tj /T1_4 10.96 Tf 9.3 0 Td (=)Tj /T1_1 10.96 Tf 11.76 0 Td (2)Tj 5.48 0 Td [(.)-385(The)-384(\002rst)-384(one)-384(is)-384(an)-384(Epanechnik)9(o)15(v-)]TJ -76.4 -12.42 Td [(type)-250(k)9(ernel)-249(function)-250(de\002ned)-250(by)]TJ /T1_3 10.96 Tf 19.11 -32.77 Td (f)Tj /T1_3 8.11 Tf 3.11 -1.64 Td (t)Tj /T1_4 10.96 Tf 3.31 1.64 Td (\()Tj /T1_3 10.96 Tf 4.25 0 Td (x)Tj /T1_4 10.96 Tf 4.89 0 Td [(\))-221(=)]TJ /T1_5 10.96 Tf 17.64 18.74 Td (\()Tj /T1_3 10.96 Tf 8.82 -11.52 Td (b)Tj /T1_6 10.96 Tf 7 0 Td (\242)Tj /T1_4 10.96 Tf 4.55 0 Td (\()Tj /T1_3 10.96 Tf 4.25 0 Td (a)Tj /T1_1 8.11 Tf 5.48 3.98 Td (2)Tj /T1_6 10.96 Tf 6.07 -3.98 Td [(\241)-138(k)]TJ /T1_3 10.96 Tf 15.52 0 Td (x)Tj /T1_6 10.96 Tf 6.41 0 Td (\241)Tj /T1_3 10.96 Tf 9.77 0 Td (t)Tj /T1_6 10.96 Tf 3.79 0 Td (k)Tj /T1_1 8.11 Tf 5.47 3.98 Td (2)Tj 0 -7.18 TD (2)Tj /T1_4 10.96 Tf 4.56 3.2 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (;)Tj /T1_6 10.96 Tf 13.99 0 Td (k)Tj /T1_3 10.96 Tf 5.47 0 Td (x)Tj /T1_6 10.96 Tf 6.42 0 Td (\241)Tj /T1_3 10.96 Tf 9.76 0 Td (t)Tj /T1_6 10.96 Tf 3.79 0 Td (k)Tj /T1_1 8.11 Tf 5.48 -1.65 Td (2)Tj /T1_6 10.96 Tf 6.99 1.65 Td (\267)Tj /T1_3 10.96 Tf 10.95 0 Td (a)Tj /T1_1 10.96 Tf -139.97 -14.94 Td (0)Tj /T1_7 10.96 Tf 5.47 0 Td (;)Tj /T1_1 10.96 Tf 85.64 0 Td (otherwise)Tj /T1_7 10.96 Tf 42.59 0 Td (;)Tj /T1_1 10.96 Tf 30.4 7.72 Td (\(3\))Tj -225.23 -32.46 Td (where)Tj /T1_3 10.96 Tf 29.15 0 Td (a)Tj /T1_7 10.96 Tf 7.59 0 Td (>)Tj /T1_1 10.96 Tf 10.62 0 Td (0)Tj 7.87 0 Td (and)Tj /T1_3 10.96 Tf 18.21 0 Td (b)Tj /T1_7 10.96 Tf 7.59 0 Td (>)Tj /T1_1 10.96 Tf 10.62 0 Td (0)Tj 5.48 0 Td [(,)-217(whereas)-218(for)-218(the)-218(second)-218(one,)-218(we)]TJ -97.13 -12.42 Td [(tak)9(e)]TJ /T1_3 10.96 Tf 2.58 -20.07 Td (f)Tj /T1_4 8.11 Tf 3.32 -2.31 Td (\()Tj /T1_3 8.11 Tf 2.94 0 Td (t)Tj /T1_1 6.57 Tf 2.26 -1.61 Td (1)Tj /T1_7 8.11 Tf 3.78 1.61 Td (;)Tj /T1_3 8.11 Tf 2.04 0 Td (t)Tj /T1_1 6.57 Tf 2.26 -1.61 Td (2)Tj /T1_4 8.11 Tf 3.78 1.61 Td (\))Tj /T1_4 10.96 Tf 3.65 2.31 Td (\()Tj /T1_3 10.96 Tf 4.25 0 Td (x)Tj /T1_1 8.11 Tf 4.86 -1.65 Td (1)Tj /T1_7 10.96 Tf 4.55 1.65 Td (;)Tj /T1_3 10.96 Tf 4.25 0 Td (x)Tj /T1_1 8.11 Tf 4.87 -1.65 Td (2)Tj /T1_4 10.96 Tf 4.55 1.65 Td [(\))-221(=)]TJ /T1_3 10.96 Tf 17.63 0 Td (b)Tj /T1_4 10.96 Tf 5.48 0 Td (\()Tj /T1_3 10.96 Tf 4.25 0 Td (a)Tj /T1_6 10.96 Tf 7 0 Td [(\241)-138(j)]TJ /T1_3 10.96 Tf 13.07 0 Td (x)Tj /T1_1 8.11 Tf 4.86 -1.65 Td (1)Tj /T1_6 10.96 Tf 6.08 1.65 Td (\241)Tj /T1_3 10.96 Tf 9.76 0 Td (t)Tj /T1_1 8.11 Tf 3.04 -1.65 Td (1)Tj /T1_6 10.96 Tf 4.55 1.65 Td (j)Tj /T1_4 10.96 Tf 3.04 0 Td (\)\()Tj /T1_3 10.96 Tf 8.5 0 Td (a)Tj /T1_6 10.96 Tf 7 0 Td [(\241)-138(j)]TJ /T1_3 10.96 Tf 13.07 0 Td (x)Tj /T1_1 8.11 Tf 4.86 -1.65 Td (2)Tj /T1_6 10.96 Tf 6.08 1.65 Td (\241)Tj /T1_3 10.96 Tf 9.76 0 Td (t)Tj /T1_1 8.11 Tf 3.04 -1.65 Td (2)Tj /T1_6 10.96 Tf 4.55 1.65 Td (j)Tj /T1_4 10.96 Tf 3.04 0 Td (\))Tj /T1_6 10.96 Tf -124.39 -17.04 Td (\242)Tj /T1_1 10.96 Tf 4.56 0 Td [(1)258(I)]TJ /T1_6 8.11 Tf 6.29 -2.24 Td (f)Tj /T1_3 8.11 Tf 4.06 0 Td (a)Tj /T1_6 8.11 Tf 4.05 0 Td (\241j)Tj /T1_3 8.11 Tf 8.55 0 Td (x)Tj /T1_1 6.57 Tf 3.59 -1.61 Td (1)Tj /T1_6 8.11 Tf 3.79 1.61 Td (\241)Tj /T1_3 8.11 Tf 6.1 0 Td (t)Tj /T1_1 6.57 Tf 2.25 -1.61 Td (1)Tj /T1_6 8.11 Tf 3.78 1.61 Td (j\270)Tj /T1_1 8.11 Tf 8.55 0 Td (0)Tj /T1_7 8.11 Tf 4.05 0 Td (;)Tj /T1_3 8.11 Tf 4.28 0 Td (a)Tj /T1_6 8.11 Tf 4.05 0 Td (\241j)Tj /T1_3 8.11 Tf 8.54 0 Td (x)Tj /T1_1 6.57 Tf 3.6 -1.61 Td (2)Tj /T1_6 8.11 Tf 3.79 1.61 Td (\241)Tj /T1_3 8.11 Tf 6.1 0 Td (t)Tj /T1_1 6.57 Tf 2.25 -1.61 Td (2)Tj /T1_6 8.11 Tf 3.78 1.61 Td (j\270)Tj /T1_1 8.11 Tf 8.55 0 Td (0)Tj /T1_6 8.11 Tf 4.05 0 Td (g)Tj /T1_4 10.96 Tf 4.55 2.24 Td (\()Tj /T1_3 10.96 Tf 4.26 0 Td (x)Tj /T1_1 8.11 Tf 4.86 -1.65 Td (1)Tj /T1_7 10.96 Tf 4.55 1.65 Td (;)Tj /T1_3 10.96 Tf 4.25 0 Td (x)Tj /T1_1 8.11 Tf 4.87 -1.65 Td (2)Tj /T1_4 10.96 Tf 4.55 1.65 Td (\))Tj /T1_1 10.96 Tf 10.85 8 Td (\(4\))Tj -219.56 -31.04 Td (where)Tj /T1_3 10.96 Tf 32.29 0 Td (a)Tj /T1_7 10.96 Tf 9.47 0 Td (>)Tj /T1_1 10.96 Tf 12.49 0 Td (0)Tj 11.01 0 Td (and)Tj /T1_3 10.96 Tf 21.35 0 Td (b)Tj /T1_7 10.96 Tf 9.46 0 Td (>)Tj /T1_1 10.96 Tf 12.5 0 Td (0)Tj 5.48 0 Td [(.)-506(Examples)-504(of)-505(both)-505(k)9(ernel)]TJ -114.05 -12.42 Td [(functions)-250(are)-250(plotted)-250(in)-250(Figure)-250(1.)]TJ 1.19 -179.63 Td (+)Tj ET q 0.4763 0 0 0.4763 67.1687 356.2364 cm /Fm0 Do Q BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 97.98 -425.96 Td (\(a\))Tj ET q 0.4763 0 0 0.4763 62.7075 170.7955 cm /Fm1 Do Q BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 97.68 -611.36 Td (\(b\))Tj -112.62 -18.43 Td [(Fig.)-554(1.)]TJ /T1_3 10.96 Tf 37.74 0 Td [(The)-554(Epanec)14(hnik)10(o)10(v-type)-553(k)9(ernel)-554(function)-554(\(3\))]TJ -37.74 -12.45 Td [(\(sub\002gur)36(e)-361(\(a\)\))-362(and)-362(the)-362(k)9(ernel)-361(function)-362(\(4\))-362(\(sub\002gur)36(e)]TJ 0 -12.45 TD (\(b\)\).)Tj /T1_1 10.96 Tf 0 -18.65 TD [(The)-228(main)-229(dif)24(ference)-228(between)-229(these)-229(tw)9(o)-228(types)-229(of)-229(k)9(ernel)]TJ 0 -12.42 TD [(functions)-344(is)-345(that)-344(one)-345(can)-344(deri)24(v)15(e)-344(a)-345(simple)-344(formula)-345(for)]TJ 0 -12.43 TD [(the)-250(inte)14(gral)-249(of)-250(\(4\))-251(o)14(v)15(er)-249(squares,)-250(b)19(ut)-250(not)-250(for)-250(the)-251(inte)14(gral)]TJ 255.01 676.28 Td [(of)-278(\(3\).)-278(This)-278(does)-278(not)-279(af)24(fect)-277(the)-278(step)-278(function)-279(approach)]TJ 0 -12.59 TD [(since)-341(the)-342(k)9(ernel)-341(functions)-342(are)-341(only)-342(e)24(v)25(aluated)-341(there)-342(at)]TJ 0 -12.58 TD [(the)-341(points)]TJ /T1_2 10.96 Tf 1.0003 0 0.1671 1.0003 312.1359 722.7971 Tm 47.67 0 Td (x)Tj /T1_3 8.11 Tf 1.0003 0 0 1.0003 359.819 722.7971 Tm 5.4 -1.82 Td (k)Tj /T1_1 10.96 Tf 4.23 1.82 Td [(,)-342(b)19(ut)-341(it)-342(does)-342(af)24(fect)-341(the)-342(w)9(a)20(v)15(elet)-341(approach)]TJ -57.3 -12.59 Td [(because)-337(the)-338(input)-338(v)14(ector)-337(consists)-337(of)-338(such)-338(inte)14(grals)-337(of)]TJ T* [(\(3\))-263(and)-263(\(4\))-263(o)14(v)15(er)-262(squares.)-263(Therefore,)-263(we)-263(ha)19(v)15(e)-262(to)-264(e)14(xpect)]TJ 0 -12.59 TD [(a)-196(loss)-196(in)-197(computational)-197(performance)-196(for)-197(k)9(ernel)-195(\(3\))-197(with)]TJ T* [(the)-249(w)9(a)20(v)15(elet)-249(approach)-250(in)-250(this)-250(case.)]TJ 0 -19.71 TD [(Both)-596(functions)-597(\(3\))-597(and)-597(\(4\))-597(are)-597(H)]TJ 164.89 0.05 Td (\250)Tj -0.91 -0.05 Td [(older)20(-continuous)]TJ -163.98 -12.59 Td [(with)-555(parameters)]TJ /T1_4 10.96 Tf 79.73 0 Td (\()Tj /T1_3 10.96 Tf 3.7 0 Td (C)Tj /T1_1 8.11 Tf 7.03 -1.65 Td (1)Tj /T1_7 10.96 Tf 4.55 1.65 Td (;)Tj /T1_2 10.96 Tf 1.0003 0 0.1671 1.0003 407.172 640.1244 Tm 4.26 0 Td (g)Tj /T1_1 8.11 Tf 1.0003 0 0 1.0003 411.4332 640.1244 Tm 4.5 -1.65 Td (1)Tj /T1_4 10.96 Tf 4.55 1.65 Td [(\))-391(=)-391(\()]TJ /T1_1 10.96 Tf 25.61 0 Td (2)Tj /T1_3 10.96 Tf 5.48 0 Td (ab)Tj /T1_7 10.96 Tf 10.95 0 Td (;)Tj /T1_1 10.96 Tf 4.26 0 Td (1)Tj /T1_4 10.96 Tf 5.47 0 Td (\))Tj /T1_1 10.96 Tf 10.35 0 Td (and)Tj /T1_4 10.96 Tf 21.91 0 Td (\()Tj /T1_3 10.96 Tf 3.7 0 Td (C)Tj /T1_1 8.11 Tf 7.04 -1.65 Td (2)Tj /T1_7 10.96 Tf 4.55 1.65 Td (;)Tj /T1_2 10.96 Tf 1.0003 0 0.1671 1.0003 519.833 640.1244 Tm 4.25 0 Td (g)Tj /T1_1 8.11 Tf 1.0003 0 0 1.0003 524.0841 640.1244 Tm 4.5 -1.65 Td (2)Tj /T1_4 10.96 Tf 4.55 1.65 Td [(\))-391(=)]TJ -220.94 -13.79 Td (\()Tj /T1_6 10.96 Tf 4.25 9.2 Td (p)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 0 G 0.43 w 10 M 0 j 0 J []0 d 253.45 -134.1 m 258.92 -134.1 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 253.45 -143.52 Td (2)Tj /T1_3 10.96 Tf 5.47 0 Td (ab)Tj /T1_7 10.96 Tf 10.96 0 Td (;)Tj /T1_1 10.96 Tf 4.25 0 Td (1)Tj /T1_4 10.96 Tf 5.48 0 Td (\))Tj /T1_1 10.96 Tf 4.25 0 Td [(,)-299(respecti)24(v)15(ely)65(.)-299(W)79(e)-298(\002x)14(ed)]TJ /T1_2 10.96 Tf 1.0003 0 0.1671 1.0003 355.938 626.3306 Tm 106.47 0 Td (a)Tj /T1_4 10.96 Tf 1.0003 0 0 1.0003 462.4372 626.3306 Tm 10.56 0 Td (=)Tj /T1_1 10.96 Tf 11.25 0 Td (1)Tj /T1_7 10.96 Tf 5.48 0 Td (:)Tj /T1_1 10.96 Tf 3.03 0 Td (1)Tj 5.48 0 Td (,)Tj /T1_2 10.96 Tf 1.0003 0 0.1671 1.0003 498.247 626.3306 Tm 6.02 0 Td (b)Tj /T1_4 10.96 Tf 1.0003 0 0 1.0003 504.2687 626.3306 Tm 10.1 0 Td (=)Tj /T1_1 10.96 Tf 11.25 0 Td (0)Tj 8.75 0 Td (and)Tj /T1_4 10.96 Tf -222.18 -12.58 Td ([)Tj /T1_6 10.96 Tf 3.03 0 Td (\241)Tj /T1_3 10.96 Tf 8.52 0 Td (T)Tj /T1_7 10.96 Tf 6.67 0 Td (;)Tj /T1_3 10.96 Tf 4.25 0 Td (T)Tj /T1_4 10.96 Tf 7.48 0 Td (])Tj /T1_1 8.11 Tf 3.04 3.98 Td (2)Tj /T1_4 10.96 Tf 6.98 -3.98 Td [(=)-221([)]TJ /T1_6 10.96 Tf 13.99 0 Td (\241)Tj /T1_1 10.96 Tf 8.51 0 Td (1)Tj /T1_7 10.96 Tf 5.48 0 Td (;)Tj /T1_1 10.96 Tf 4.25 0 Td (1)Tj /T1_4 10.96 Tf 5.48 0 Td (])Tj /T1_1 8.11 Tf 3.03 3.98 Td (2)Tj /T1_1 10.96 Tf 7.29 -3.98 Td [(for)-250(both)-250(types)-250(of)-250(k)9(ernel)-249(functions.)]TJ -88 -19.72 Td [(F)15(or)-514(the)-515(remaining)-515(parameters,)-515(we)-515(started)-515(with)-515(the)]TJ 0 -12.58 TD [(follo)25(wing)-534(con\002guration:)]TJ /T1_3 10.96 Tf 115.52 0 Td (b)Tj /T1_4 10.96 Tf 9.64 0 Td (=)Tj /T1_1 10.96 Tf 12.68 0 Td (1)Tj 5.47 0 Td (,)Tj /T1_3 10.96 Tf 8.6 0 Td (a)Tj /T1_4 10.96 Tf 9.64 0 Td (=)Tj /T1_1 10.96 Tf 12.68 0 Td (1)Tj 11.33 0 Td (and)Tj /T1_2 10.96 Tf 1.0003 0 0.1671 1.0003 497.7469 581.4383 Tm 21.67 0 Td (e)Tj /T1_4 10.96 Tf 1.0003 0 0 1.0003 519.4229 581.4383 Tm 9.88 0 Td (=)Tj /T1_1 10.96 Tf 12.68 0 Td (1)Tj 5.48 0 Td (.)Tj -235.27 -12.59 Td [(Furthermore,)-385(we)-385(di)24(vided)]TJ /T1_4 10.96 Tf 115.53 0 Td ([)Tj /T1_6 10.96 Tf 3.04 0 Td (\241)Tj /T1_1 10.96 Tf 8.51 0 Td (1)Tj /T1_7 10.96 Tf 5.48 0 Td (;)Tj /T1_1 10.96 Tf 4.25 0 Td (1)Tj /T1_4 10.96 Tf 5.48 0 Td (])Tj /T1_1 8.11 Tf 3.03 3.98 Td (2)Tj /T1_1 10.96 Tf 8.77 -3.98 Td [(into)-385(an)-385(equidistant)]TJ -154.09 -12.59 Td [(grid)-279(of)]TJ 32.89 0 Td (50)Tj /T1_6 10.96 Tf 12.6 0 Td (\243)Tj /T1_1 10.96 Tf 10.15 0 Td (50)Tj 14.01 0 Td [(points)-279(and)-279(chose)]TJ /T1_3 10.96 Tf 76.73 0 Td (l)Tj /T1_4 10.96 Tf 6.22 0 Td (=)Tj /T1_1 10.96 Tf 11.12 0 Td (0)Tj 8.54 0 Td [(for)-278(the)-279(number)]TJ -172.26 -12.58 Td [(of)-252(detail)-253(le)24(v)15(els)-252(to)-253(be)-252(increased.)-253(T)79(w)10(o)-252(realisations)-253(of)-253(the)]TJ 0 -12.59 TD (1)Tj 5.48 0 Td [(-stable)-373(random)-374(\002eld)]TJ /T1_3 10.96 Tf 94.45 0 Td (X)Tj /T1_1 10.96 Tf 11.82 0 Td [(with)-374(k)9(ernels)-373(\(3\))-374(and)-374(\(4\))-375(are)]TJ -111.75 -12.58 Td [(sho)25(wn)-249(in)-250(Figure)-250(2.)]TJ ET q 0.7157 0 0 0.7157 343.2245 360.5876 cm /Fm2 Do Q BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 339.25 -421.78 Td (\(a\))Tj ET q 0.698 0 0 0.698 343.2245 197.6529 cm /Fm3 Do Q BT /T1_1 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 339.25 -584.67 Td (\(b\))Tj -99.18 -18.42 Td [(Fig.)-369(2.)]TJ /T1_3 10.96 Tf 33.68 0 Td [(T)74(wo)-369(r)36(ealisations)-369(of)-369(stable)-370(r)14(andom)-369(\002elds)-369(with)]TJ -33.68 -12.45 Td [(k)10(ernel)-203(\(3\))-204(\(sub\002gur)36(e)-203(\(a\)\))-203(and)-204(k)9(ernel)-203(\(4\))-204(\(sub\002gur)36(e)-203(\(b\)\).)]TJ /T1_1 10.96 Tf 0 -19.72 TD [(First,)-492(we)-492(k)9(ept)-492(all)-492(parameters)-493(\002x)14(ed)-491(and)-493(determined)]TJ 0 -12.58 TD [(the)-593(computational)-593(time)-593(depending)-593(on)-593(the)-594(number)]TJ 0 -12.59 TD [(of)-399(realisations.)-401(F)14(or)-399(the)-399(step)-400(function)-400(approach,)-400(each)]TJ T* [(realisation)-236(needs)-237(the)-237(same)-237(computational)-237(time.)-237(F)14(or)-236(the)]TJ 0 -12.58 TD [(w)10(a)20(v)15(elet)-456(approach,)-457(ho)24(we)25(v)15(er)40(,)-456(the)-457(w)9(a)20(v)15(elet)-456(coef)24(\002cients)]TJ 0 -12.59 TD [(only)-525(ha)19(v)15(e)-525(to)-526(be)-526(calculated)-526(for)-526(the)-526(\002rst)-526(realisation)]TJ -11.24 -34.86 Td (7)Tj ET endstream endobj 128 0 obj 12372 endobj 129 0 obj << /Length 130 0 R >> stream 0 g 1 i /RelativeColorimetric ri BT /T1_0 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm -14.94 -21.91 Td [(Consider)-250(the)-250(so-called)-250(\002rst-order)-250(madogram)]TJ /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 57.0559 747.974 Tm 7.19 -24.4 Td (g)Tj /T1_2 10.96 Tf 1.0003 0 0 1.0003 60.1767 723.5673 Tm 5.41 0 Td (\()Tj /T1_3 10.96 Tf 4.25 0 Td (h)Tj /T1_2 10.96 Tf 5.48 0 Td [(\))-908(=)]TJ /T1_4 10.96 Tf 32.68 0 Td (E)Tj /T1_5 10.96 Tf 7.31 0 Td (j)Tj /T1_3 10.96 Tf 3.03 0 Td (X)Tj /T1_2 10.96 Tf 7.73 0 Td (\()Tj /T1_3 10.96 Tf 3.97 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_5 10.96 Tf 5.78 0 Td (\241)Tj /T1_3 10.96 Tf 10.03 0 Td (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_3 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 5.31 0 Td (+)Tj /T1_3 10.96 Tf 10.04 0 Td (h)Tj /T1_2 10.96 Tf 5.48 0 Td (\))Tj /T1_5 10.96 Tf 4.25 0 Td (j)Tj /T1_2 10.96 Tf -96.89 -29.18 Td (=)Tj /T1_3 10.96 Tf 18.47 0 Td (b)Tj /T1_0 10.96 Tf 18.59 7.41 Td (1)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 0 G 0.44 w 10 M 0 j 0 J []0 d 42.67 -72.76 m 71.97 -72.76 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_5 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 42.67 -75.14 Td (p)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 0.43 w 51.8 -74.93 m 64.18 -74.93 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_0 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 51.8 -84.25 Td (2)Tj /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 123.8142 685.6169 Tm 5.48 0 Td [(p)-80(s)]TJ /T1_4 10.96 Tf 1.0003 0 0 1.0003 129.2957 685.6169 Tm 15.88 8.76 Td (E)Tj /T1_6 10.96 Tf 8.52 22.45 Td (\257)Tj 0 -6.57 TD (\257)Tj T* (\257)Tj 0 -6.58 TD (\257)Tj 0 -6.57 TD (\257)Tj T* (\257)Tj /T1_6 9.86 Tf 6.39 24.09 Td (Z)Tj /T1_4 8.11 Tf -2.09 -30.47 Td (R)Tj /T1_0 6.57 Tf 5.86 2.35 Td (2)Tj /T1_6 10.96 Tf 7.29 26.6 Td (\263)Tj /T1_3 10.96 Tf 6.54 -12.16 Td (e)Tj /T1_5 8.11 Tf 4.86 6.06 Td (\241)Tj /T1_0 6.57 Tf 11.73 3.2 Td (1)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 0.32 w 118.03 -67.4 m 129.77 -67.4 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_0 6.57 Tf 1.0003 0 0 1.0003 72 769.89 Tm 118.03 -74.18 Td (2)Tj /T1_1 6.57 Tf 1.0003 0 0.1671 1.0003 190.0624 695.6896 Tm 3.28 0 Td (s)Tj /T1_0 6.57 Tf 1.0003 0 0 1.0003 193.3433 695.6896 Tm 4.68 1.9 Td (2)Tj /T1_5 8.11 Tf 4.98 2.85 Td (k)Tj /T1_3 8.11 Tf 4.05 0 Td (x)Tj /T1_5 8.11 Tf 3.62 0 Td (\241)Tj /T1_3 8.11 Tf 6.1 0 Td (t)Tj /T1_5 8.11 Tf 2.81 0 Td (k)Tj /T1_0 6.57 Tf 4.05 2.95 Td (2)Tj 0 -5.7 TD (2)Tj /T1_5 10.96 Tf -42.36 -38.84 Td (\241)Tj /T1_3 10.96 Tf 8.51 0 Td (e)Tj /T1_5 8.11 Tf 4.86 6.07 Td (\241)Tj /T1_0 6.57 Tf 11.73 3.2 Td (1)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 130.11 -102.92 m 141.85 -102.92 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_0 6.57 Tf 1.0003 0 0 1.0003 72 769.89 Tm 130.11 -109.7 Td (2)Tj /T1_1 6.57 Tf 1.0003 0 0.1671 1.0003 202.1457 660.1599 Tm 3.29 0 Td (s)Tj /T1_0 6.57 Tf 1.0003 0 0 1.0003 205.4366 660.1599 Tm 4.67 1.9 Td (2)Tj /T1_5 8.11 Tf 4.98 2.85 Td (k)Tj /T1_3 8.11 Tf 4.05 0 Td (x)Tj /T1_5 8.11 Tf 3.63 0 Td (\241)Tj /T1_3 8.11 Tf 6.09 0 Td (t)Tj /T1_5 8.11 Tf 2.81 0 Td (\241)Tj /T1_3 8.11 Tf 6.3 0 Td (h)Tj /T1_5 8.11 Tf 4.05 0 Td (k)Tj /T1_0 6.57 Tf 4.05 2.95 Td (2)Tj T* (2)Tj /T1_6 10.96 Tf 4.29 8.85 Td (\264)Tj /T1_3 10.96 Tf 7.75 -12.17 Td (M)Tj /T1_2 10.96 Tf 9.57 0 Td (\()Tj /T1_3 10.96 Tf 4.25 0 Td [(d)-51(x)]TJ /T1_2 10.96 Tf 10.94 0 Td (\))Tj /T1_6 10.96 Tf 4.26 12.6 Td (\257)Tj 0 -6.57 TD (\257)Tj T* (\257)Tj /T1_2 10.96 Tf -197.56 -27.15 Td (=)Tj /T1_3 10.96 Tf 19.66 8.37 Td (c)Tj /T1_1 8.11 Tf 1.0003 0 0.1671 1.0003 109.2002 639.5142 Tm 5.25 -2.27 Td (a)Tj /T1_7 8.11 Tf 1.0003 0 0 1.0003 114.0715 637.2436 Tm 5.79 0 Td (;)Tj /T1_1 8.11 Tf 1.0003 0 0.1671 1.0003 119.8631 637.2436 Tm 2.24 0 Td (b)Tj /T1_3 6.57 Tf 1.0003 0 0 1.0003 122.1038 637.2436 Tm 4.29 -1.21 Td (t)Tj /T1_2 10.96 Tf 3.27 3.48 Td (\()Tj /T1_0 10.96 Tf 4.25 0 Td (1)Tj /T1_2 10.96 Tf 5.48 0 Td (\))Tj /T1_3 10.96 Tf 4.25 0 Td (b)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 0.44 w 37.19 -135.97 m 77.11 -135.97 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_5 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 42.5 -138.36 Td (p)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 0.43 w 51.63 -138.14 m 64.01 -138.14 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_0 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 51.63 -147.46 Td (2)Tj /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 123.6442 622.3895 Tm 5.48 0 Td [(p)-80(s)]TJ /T1_6 9.86 Tf 1.0003 0 0 1.0003 129.1257 622.3895 Tm 22.41 22.44 Td (Z)Tj /T1_4 8.11 Tf -2.09 -30.47 Td (R)Tj /T1_0 6.57 Tf 5.86 2.34 Td (2)Tj /T1_6 10.96 Tf 7.29 27.04 Td (\257)Tj T* (\257)Tj T* (\257)Tj /T1_3 10.96 Tf 3.64 0.54 Td (e)Tj /T1_5 8.11 Tf 4.87 6.07 Td (\241)Tj /T1_0 6.57 Tf 11.72 3.2 Td (1)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 0.32 w 106.58 -130.61 m 118.33 -130.61 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_0 6.57 Tf 1.0003 0 0 1.0003 72 769.89 Tm 106.58 -137.39 Td (2)Tj /T1_1 6.57 Tf 1.0003 0 0.1671 1.0003 178.6093 632.4623 Tm 3.29 0 Td (s)Tj /T1_0 6.57 Tf 1.0003 0 0 1.0003 181.9002 632.4623 Tm 4.67 1.9 Td (2)Tj /T1_5 8.11 Tf 4.98 2.85 Td (k)Tj /T1_3 8.11 Tf 4.06 0 Td (x)Tj /T1_5 8.11 Tf 3.62 0 Td (\241)Tj /T1_3 8.11 Tf 6.1 0 Td (t)Tj /T1_5 8.11 Tf 2.8 0 Td (k)Tj /T1_0 6.57 Tf 4.06 2.95 Td (2)Tj 0 -5.7 TD (2)Tj /T1_5 10.96 Tf -32.12 -38.84 Td (\241)Tj /T1_3 10.96 Tf 8.51 0 Td (e)Tj /T1_5 8.11 Tf 4.87 6.07 Td (\241)Tj /T1_0 6.57 Tf 11.72 3.19 Td (1)Tj ET 1.0003 0 0 1.0003 72 769.89 cm 128.91 -166.13 m 140.66 -166.13 l S 0.9997 0 0 0.9997 -71.9802 -769.6786 cm BT /T1_0 6.57 Tf 1.0003 0 0 1.0003 72 769.89 Tm 128.91 -172.92 Td (2)Tj /T1_1 6.57 Tf 1.0003 0 0.1671 1.0003 200.9454 596.9225 Tm 3.29 0 Td (s)Tj /T1_0 6.57 Tf 1.0003 0 0 1.0003 204.2363 596.9225 Tm 4.67 1.9 Td (2)Tj /T1_5 8.11 Tf 4.98 2.86 Td (k)Tj /T1_3 8.11 Tf 4.06 0 Td (x)Tj /T1_5 8.11 Tf 3.62 0 Td (\241)Tj /T1_3 8.11 Tf 6.1 0 Td (t)Tj /T1_5 8.11 Tf 2.8 0 Td (\241)Tj /T1_3 8.11 Tf 6.3 0 Td (h)Tj /T1_5 8.11 Tf 4.06 0 Td (k)Tj /T1_0 6.57 Tf 4.05 2.94 Td (2)Tj 0 -5.69 TD (2)Tj /T1_6 10.96 Tf 4.28 9.28 Td (\257)Tj 0 -6.57 TD (\257)Tj 0 -6.58 TD (\257)Tj /T1_3 10.96 Tf 4.87 0.55 Td [(d)-51(x)]TJ /T1_7 10.96 Tf 10.94 0 Td (:)Tj /T1_0 10.96 Tf -207.87 -27.48 Td [(which)-267(does)-267(only)-267(depend)-268(on)-267(the)-267(length)-268(of)]TJ /T1_3 10.96 Tf 182.26 0 Td (h)Tj /T1_0 10.96 Tf 5.48 0 Td [(,)-267(b)19(ut)-266(not)-268(on)]TJ -187.74 -12.58 Td [(the)-285(orientation.)-286(It)-285(e)14(xists)-285(since)]TJ /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 57.0559 555.5412 Tm 133.24 0 Td (a)Tj /T1_7 10.96 Tf 1.0003 0 0 1.0003 190.3325 555.5412 Tm 10.47 0 Td (>)Tj /T1_0 10.96 Tf 11.16 0 Td (1)Tj 5.48 0 Td [(.)-285(W)79(e)-285(note)-285(that)-286(we)]TJ -160.35 -12.58 Td [(cannot)-209(tak)9(e)-209(the)-209(v)24(ariogram)-209(as)-210(described)-209(in)-210(W)79(ack)10(ernagel)]TJ 0 -12.58 TD [(\(1998\))-386(since)-386(for)]TJ /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 57.0559 530.3742 Tm 77.19 0 Td (a)Tj /T1_7 10.96 Tf 1.0003 0 0 1.0003 134.2671 530.3742 Tm 11.08 0 Td (<)Tj /T1_0 10.96 Tf 11.78 0 Td (2)Tj 5.47 0 Td [(,)-386(the)-386(second)-386(moment)-386(of)]TJ /T1_3 10.96 Tf 112.74 0 Td (X)Tj /T1_2 10.96 Tf 7.73 0 Td (\()Tj /T1_3 10.96 Tf 3.97 0 Td (t)Tj /T1_2 10.96 Tf 3.8 0 Td (\))Tj /T1_0 10.96 Tf -233.76 -12.58 Td [(does)-250(not)-250(e)14(xist)-249(for)-250(each)]TJ /T1_3 10.96 Tf 100.88 0 Td (t)Tj /T1_5 10.96 Tf 6.23 0 Td (2)Tj /T1_3 10.96 Tf 9.73 0 Td (A)Tj /T1_0 10.96 Tf 6.69 0 Td (.)Tj -123.53 -19.67 Td [(One)-625(can)-626(think)-626(of)-626(the)-625(\002rst-order)-626(madogram)-626(as)-626(a)]TJ T* [(measure)-227(of)-227(dissimilarity)-228(between)-227(the)-227(random)-228(v)24(ariables)]TJ /T1_3 10.96 Tf T* (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_3 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_0 10.96 Tf 9.17 0 Td (and)Tj /T1_3 10.96 Tf 20.74 0 Td (X)Tj /T1_2 10.96 Tf 7.73 0 Td (\()Tj /T1_3 10.96 Tf 3.97 0 Td (t)Tj /T1_2 10.96 Tf 6.12 0 Td (+)Tj /T1_3 10.96 Tf 10.84 0 Td (h)Tj /T1_2 10.96 Tf 5.48 0 Td (\))Tj /T1_0 10.96 Tf 9.17 0 Td [(depending)-449(on)-449(the)-449(distance)]TJ /T1_5 10.96 Tf 125.57 0 Td (k)Tj /T1_3 10.96 Tf 5.48 0 Td (h)Tj /T1_5 10.96 Tf 5.48 0 Td (k)Tj /T1_0 8.11 Tf 5.48 -1.65 Td (2)Tj /T1_0 10.96 Tf 4.55 1.65 Td (.)Tj -235.27 -12.58 Td [(W)79(e)-312(calculated)-313(the)-314(corresponding)-313(empirical)-313(v)14(ersion)-313(of)]TJ T* [(the)-281(\002rst-order)-281(madogram)-282(\226)-281(the)-281(so-called)-282(e)14(xperimental)]TJ T* [(\002rst-order)-315(madogram)-316(\226)-316(as)-315(correspondingly)-316(de\002ned)-316(in)]TJ T* [(W)79(ack)10(ernagel)-354(\(1998\))-355(and)-355(\002tted)-355(the)-355(theoretical)-356(one)-355(by)]TJ T* [(the)-225(least)-226(squares)-226(method)-226(to)-225(the)-226(empirical)-226(one.)-226(Both)-226(the)]TJ 0 -12.57 TD [(theoretical)-271(and)-271(e)14(xperimental)-270(\002rst-order)-272(madogram)-271(are)]TJ 0 -12.58 TD [(plotted)-250(in)-250(Figure)-250(3.)]TJ ET q 0.5502 0 0 0.5502 62.7075 172.4059 cm /Fm0 Do Q BT /T1_0 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm -14.94 -615.75 Td [(Fig.)-268(3.)]TJ /T1_3 10.96 Tf 31.45 0 Td [(Theor)37(etical)-267(\(r)36(ed)-268(curve\))-268(and)-268(e)19(xperimental)-267(\(blue)]TJ -31.45 -12.45 Td [(dots\))-250(\002r)9(st-or)37(der)-249(mado)9(gr)15(am.)]TJ /T1_0 10.96 Tf 0 -19.67 TD [(From)-631(the)-632(least)-631(squares)-632(method,)-632(we)-631(obtained)-632(the)]TJ 0 -12.58 TD (estimates)Tj 44.84 2.61 Td (\210)Tj /T1_3 10.96 Tf -0.92 -2.61 Td (b)Tj /T1_2 10.96 Tf 8.14 0 Td (=)Tj /T1_0 10.96 Tf 11.17 0 Td (10)Tj /T1_7 10.96 Tf 10.96 0 Td (:)Tj /T1_0 10.96 Tf 3.03 0 Td (7055)Tj 25.06 0 Td (and)Tj 21.31 0.48 Td (\210)Tj /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 180.6798 109.7387 Tm -2.27 -0.48 Td (s)Tj /T1_2 10.96 Tf 1.0003 0 0 1.0003 178.3292 109.2586 Tm 10.45 0 Td (=)Tj /T1_0 10.96 Tf 11.18 0 Td (4)Tj /T1_7 10.96 Tf 5.47 0 Td (:)Tj /T1_0 10.96 Tf 3.04 0 Td (3472)Tj 25.05 0 Td [(and)-287(simulated)]TJ -176.43 -12.58 Td (the)Tj /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 57.0559 96.6751 Tm 16.78 0 Td (a)Tj /T1_0 10.96 Tf 1.0003 0 0 1.0003 73.8405 96.6751 Tm 7.82 0 Td [(-stable)-309(random)-309(\002eld)-309(\(5\).)-310(In)-309(Figure)-309(4,)-310(a)-309(plot)-309(of)-309(a)]TJ -24.6 -12.58 Td [(realisation)-216(of)-216(the)-217(\002tted)]TJ /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 57.0559 84.0917 Tm 100.16 0 Td (a)Tj /T1_0 10.96 Tf 1.0003 0 0 1.0003 157.2434 84.0917 Tm 7.83 0 Td [(-stable)-216(random)-216(\002eld)-216(is)-217(sho)24(wn.)]TJ -107.99 -12.58 Td [(In)-417(order)-417(to)-417(be)-418(able)-417(to)-417(compare)-418(the)-417(picture)-417(with)-418(the)]TJ 255.01 676.28 Td [(real)-319(data,)-320(we)-320(used)-319(ordinary)-320(kriging)-320(\(see)-320(W)79(ack)10(ernagel)]TJ 0 -12.62 TD [(\(1998\)\))-231(to)-231(e)14(xtrapolate)-231(the)-232(de)24(viations)-230(for)-232(the)-231(year)-232(2000.)]TJ ET q 0.3349 0 0 0.3349 317.7875 608.9858 cm /Fm1 Do Q BT /T1_0 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 352.99 -173.47 Td (\(a\))Tj ET q 0.3349 0 0 0.3349 317.7875 492.2738 cm /Fm2 Do Q BT /T1_0 10.96 Tf 1.0003 0 0 1.0003 72 769.89 Tm 352.68 -290.16 Td (\(b\))Tj -112.61 -18.42 Td [(Fig.)-310(4.)]TJ /T1_3 10.96 Tf 32.38 0 Td [(Krig)9(ed)-310(de)14(viations)-310(for)-311(insur)14(ance)-309(year)-311(2000)-311(\(a\))]TJ -32.38 -12.45 Td [(and)-226(a)-226(r)36(ealisaton)-225(of)-226(the)-226(\002tted)]TJ /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 312.1359 448.7718 Tm 124.63 0 Td (a)Tj /T1_3 10.96 Tf 1.0003 0 0 1.0003 436.8002 448.7718 Tm 7.82 0 Td [(-stable)-226(r)14(andom)-225(\002eld)-226(\(b\).)]TJ /T1_0 10.96 Tf -132.45 -19.95 Td [(One)-453(can)-454(see)-454(that)-454(both)-454(maps)-454(sho)24(w)-453(a)-454(similar)-454(spatial)]TJ 0 -12.61 TD [(structure)-303(of)-303(the)-303(de)24(viations.)-303(There)-304(are)-303(some)-303(v)14(ery)-303(lar)17(ge)]TJ 0 -12.62 TD [(de)25(viations)-348(which)-349(are)-349(dominant)-348(in)-349(the)-349(maps.)-349(The)-349(f)9(act)]TJ 0 -12.61 TD [(that)-228(the)-229(kriged)-229(map)-229(is)-228(smoother)-229(than)-229(the)-229(simulated)-229(one)]TJ 0 -12.62 TD [(is)-249(due)-250(to)-250(the)-250(kriging)-250(technique.)]TJ 0 -19.94 TD [(In)-375(order)-375(to)-375(obtain)-375(a)-375(realisation)-375(of)-375(the)-375(actual)-376(a)19(v)15(erage)]TJ 0 -12.61 TD [(claim)-368(sizes)-369(in)-369(each)-368(zip)-369(code)-369(center)39(,)-367(one)-369(can)-369(add)-369(the)]TJ 0 -12.62 TD [(v)25(alues)-220(in)-220(the)-220(realisation)-220(of)-221(the)]TJ /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 312.1359 333.1601 Tm 132.26 0 Td (a)Tj /T1_0 10.96 Tf 1.0003 0 0 1.0003 444.4323 333.1601 Tm 7.82 0 Td [(-stable)-220(random)-220(\002eld)-221(to)]TJ -140.08 -12.61 Td [(the)-249(o)14(v)15(erall)-249(mean)]TJ 76.28 0 Td (\257)Tj /T1_3 10.96 Tf -0.85 0 Td (z)Tj /T1_2 10.96 Tf 4.26 0 Td (\()Tj /T1_3 10.96 Tf 3.98 0 Td (t)Tj /T1_3 8.11 Tf 3.04 -1.65 Td (i)Tj /T1_2 10.96 Tf 2.76 1.65 Td (\))Tj /T1_0 10.96 Tf 6.98 0 Td [(at)-250(each)-250(zip)-250(code)-250(center)]TJ /T1_3 10.96 Tf 102.24 0 Td (t)Tj /T1_3 8.11 Tf 3.05 -1.65 Td (i)Tj /T1_0 10.96 Tf 2.75 1.65 Td (.)Tj /T1_8 13.94 Tf -204.49 -43.29 Td [(SUMMAR)50(Y)-277(AND)-278(OUTLOOK)]TJ /T1_0 10.96 Tf 0 -27.03 TD [(W)80(e)-508(presented)-508(tw)9(o)-507(approaches)-508(to)-508(simulate)]TJ /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 312.1359 250.2073 Tm 200.97 0 Td (a)Tj /T1_0 10.96 Tf 1.0003 0 0 1.0003 513.1611 250.2073 Tm 7.83 0 Td (-stable)Tj -208.8 -12.61 Td [(random)-492(\002elds)-493(that)-493(are)-492(based)-493(on)-493(approximating)-493(the)]TJ 0 -12.62 TD [(k)10(ernel)-395(function)-396(by)-395(a)-396(step)-396(function)-396(and)-395(by)-396(a)-396(w)9(a)20(v)15(elet)]TJ 0 -12.61 TD [(series.)-326(F)14(or)-325(both)-327(approaches,)-326(we)-326(deri)24(v)15(ed)-325(estimates)-327(for)]TJ 0 -12.62 TD [(the)-249(approximation)-250(error)]TJ /T1_3 10.96 Tf 106.8 0 Td [(E)-72(r)-23(r)]TJ /T1_2 10.96 Tf 16.52 0 Td (\()Tj /T1_3 10.96 Tf 4.25 0 Td (X)Tj /T1_2 10.96 Tf 7.72 0 Td (\()Tj /T1_3 10.96 Tf 3.98 0 Td (t)Tj /T1_2 10.96 Tf 3.79 0 Td (\))Tj /T1_7 10.96 Tf 4.25 0 Td (;)Tj /T1_0 10.96 Tf 6.84 2.18 Td (\230)Tj /T1_3 10.96 Tf -2.59 -2.18 Td (X)Tj /T1_2 8.11 Tf 7.73 3.98 Td (\()Tj /T1_3 8.11 Tf 3.14 0 Td (n)Tj /T1_2 8.11 Tf 4.05 0 Td (\))Tj /T1_2 10.96 Tf 3.65 -3.98 Td (\()Tj /T1_3 10.96 Tf 3.97 0 Td (t)Tj /T1_2 10.96 Tf 3.8 0 Td [(\))1(\))]TJ /T1_0 10.96 Tf 8.5 0 Td (.)Tj -186.4 -19.94 Td [(In)-549(the)-549(simulation)-549(study)64(,)-549(we)-549(sa)14(w)-549(that)-549(for)-549(the)-550(\002rst)]TJ 0 -12.61 TD [(realisation)-640(of)-641(an)]TJ /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 312.1359 167.1745 Tm 86.17 0 Td (a)Tj /T1_0 10.96 Tf 1.0003 0 0 1.0003 398.3296 167.1745 Tm 7.82 0 Td [(-stable)-640(random)-641(\002eld,)-641(the)-641(step)]TJ -93.99 -12.62 Td [(function)-471(approach)-472(performs)-471(better)-472(than)-472(the)-472(w)9(a)20(v)15(elet)]TJ T* [(approach)-346(due)-347(to)-346(the)-347(initial)-347(calculation)-346(of)-347(the)-347(w)9(a)20(v)15(elet)]TJ 0 -12.62 TD [(coef)25(\002cients.)-674(F)14(or)-670(an)14(y)-671(further)-672(realisation,)-672(ho)24(we)25(v)15(er)40(,)]TJ 0 -12.61 TD [(the)-452(w)9(a)20(v)15(elet)-452(approach)-454(outperforms)-453(the)-453(step)-453(function)]TJ 0 -12.62 TD (approach.)Tj 0 -19.94 TD [(W)80(e)-211(then)-212(applied)-212(the)-212(simulation)-211(methods)-212(to)-212(an)-212(portfolio)]TJ 0 -12.62 TD [(of)-565(storm)-565(insurance)-565(policies)-565(by)-565(\002tting)-565(an)]TJ /T1_1 10.96 Tf 1.0003 0 0.1671 1.0003 312.1359 71.5082 Tm 200.97 0 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