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integral(W(s)^n*dW(s),0,t)
.BMItoP(N, T, power, output = FALSE)
output = TRUE
write a output
to an Excel 2007.w(0) = 0
.
The follows from the algebraic rearrangement : BMIto1
simulation of the Ito integral[1], BMIto2
simulation of the Ito integral[2], BMItoC
properties of the stochastic integral and Ito processes[3], BMItoT
properties of the stochastic integral and Ito processes[5].## if power = 1
## integral(W(s) * dW(s),0,t) = W(t)^2/2 - 1/2 * t
BMItoP(N=1000,T=1,power =1)
## if power = 2
## integral(W(s)^2 * dW(s),0,t) = W(t)^3/3 - 2/2 * integral(W(s)*ds,0,t)
BMItoP(N=1000,T=1,power =2)
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