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Sim.DiffProc (version 2.5)

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].

Examples

Run this code
BMItoT(N=1000,T=1)

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