BMItoT: Properties of the stochastic integral and Ito Process [5]
Description
Simulation of the Ito integral(s*dW(s),0,t).
Usage
BMItoT(N, T, output = FALSE)
Arguments
N
size of process.
T
final time.
output
if output = TRUE write a output to an Excel (.csv).
Value
data frame(time,Ito,sum.Ito) and plot of the Ito integral.
Details
However the Ito integral also has the peculiar property, amongst others, that : $$integral(s*dW(s),0,t) = t * W(t) - integral(W(s)*ds,0,t)$$
from classical calculus for Ito integral with w(0) = 0.
The follows from the algebraic rearrangement : $$integral(s*dW(s),0,t) = sum ( t *(W(t+1)-W(t)),0,t)$$
See Also
BMIto1 simulation of the Ito integral[1], BMIto2 simulation of the Ito integral[2], BMItoC properties of the stochastic integral and Ito processes[3], BMItoP properties of the stochastic integral and Ito processes[4].