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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
260 37 "Maple-Prozeduren (Stochastic Package)" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "read stocha
sticMVR51;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "with(stochast
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ist(algebraic),a::list(algebraic),b::list(list(algebraic)))" }}{PARA 
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0 "" {MPLTEXT 1 0 28 "  for i from 1 to nops(U) do" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 24 "    l0:=L0(U[i],a,b)*dt;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "    lj:=0;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "    \+
for k from 1 to nops(b) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "     \+
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*dt + b*X[t]*dW[t];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "itof
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{TEXT 261 18 "Berechnung von L0:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "L0(x[2],[x[1],x[2]],[[r,0],[0,r]]);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT 262 18 "Berechnung von LJ:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 25 "LJ(x[2],[[r,0],[0,r]],2);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 25 "LJ(x[2],[[r,0],[0,r]],1);" }}}{EXCHG {PARA 256 "
" 0 "" {TEXT -1 29 "Euler-Verfahren (Ordnung 0.5)" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "dX1[t]=X2[t
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38 "dX2[t]=X1[t]*dt + s*dW1[t] + r*dW2[t]:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "a1(t,X1,X2)=X2:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "a2(t,X1,X2)=X1:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "b11=r:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b1
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b22=r:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "Euler([x[2],x[1]],[[r,s],[s,r]]);" }}}{EXCHG {PARA 0 
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1 0 39 "dX1[t]=X2[t]*dt + r*dW1[t] + s*dW2[t]: " }}}{EXCHG {PARA 0 "> \+
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "a1(t,X1,X2)=X2:" }}}{EXCHG 
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{MPLTEXT 1 0 6 "b12=s:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b2
1=s:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b22=r:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Milstein([x[2],x[1]],[[r,s],[s,r]])
;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 46 "Stochastisches Taylor-Verfa
hren (Ordnung 1.5) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "dX1[
t]=X2[t]*dt + r*dW1[t] + s*dW2[t]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 38 "dX2[t]=X1[t]*dt + s*dW1[t] + r*dW2[t]:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "a1(t,X1,X2)=X2:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 15 "a2(t,X1,X2)=X1:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 6 "b11=r:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "
b12=s:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b21=s:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b22=r:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 38 "Taylor1hlf([x[2],x[1]],[[r,s],[s,r]]);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 263 43 "Stochastisches Taylor-Verfahren (Ordnung
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or2([x[2],x[1]],[[r,s],[s,r]]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 264 
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{MPLTEXT 1 0 35 "wkeuler([x[1],x[2]],[[r,0],[0,r]]);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT 265 38 "Taylor-Verfahren (schwache Ordnung 2)\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "wktay2([x[1],x[2]],[[r,0],[0
,r]]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 37 "Taylor-Verfahren (schw
ache Ordnung 3)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "dX1[t]=X
2[t]*dt + r*dW1[t] + s*dW2[t]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
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{MPLTEXT 1 0 15 "a2(t,X1,X2)=X1:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "b11=r:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b1
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b22=r:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "wktay3([x[2],x[1]],[[r,s],[s,r]]);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT 266 82 "Berechnung von L0, L1, L2 für eine stochastisc
he Differentialgleichung (d=1, m=2):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 
"read stochasticMVR51;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "w
ith(stochastic):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "value1 \+
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{MPLTEXT 1 0 12 "L := proc(F)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "  \+
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cname); v := op(F);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "  if ip = 0 \+
then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "    seq(a.k(v)*Diff(F,v[k])
, k=1..d);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "    seq(seq(seq(b.k.j
(v)*b.l.j(v)*Diff(Diff(F,v[k]),v[l]),j=1..m),l=1..d),k=1..d);" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "    Diff(F,v[d+1]) + convert([%%],`
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e" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "    convert([seq(b.k.ip*Diff(F
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "d:= 1: m := 2: L
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(\{a1(X1,t)=a*X1, b11(X1,t)=b*X1,b12(X1,t)=c*X1,U(X1,t)=X1\},%);" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "value1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
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"subs(\{a1(X1,t)=a*X1, b11(X1,t)=b*X1,b12(X1,t)=c*X1,U(X1,t)=X1\},%);
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "L2 := L[2](U(X1,t));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "subs(\{a1(X1,t)=a*X1, b11(X1
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"Berechnung der LILJ im Milstein-Verfahren:\n" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 24 "L1L1 := L[1](b11(X1,t)):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 66 "subs(\{a1(X1,t)=a*X1, b11(X1,t)=b*X1,b12(X1,t)
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "value1(%);" }}}{EXCHG {PARA 0 "> " 
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