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Sim.DiffProc (version 2.5)

BMItoC: Properties of the stochastic integral and Ito Process [3]

Description

Simulation of the Ito integral(alpha*dW(s),0,t).

Usage

BMItoC(N, T, alpha, output = FALSE)

Arguments

N
size of process.
T
final time.
alpha
constant.
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 : $$integral(alpha*dW(s),0,t) = alpha * W(t)$$ from classical calculus for Ito integral with w(0) = 0. The follows from the algebraic rearrangement : $$integral(alpha * dW(s),0,t) = sum ( alpha*(W(t+1)-W(t)),0,t)$$

See Also

BMIto1 simulation of the Ito integral[1], BMIto2 simulation of the Ito integral[2], BMItoP properties of the stochastic integral and Ito processes[4], BMItoT properties of the stochastic integral and Ito processes[5].

Examples

Run this code
BMItoC(N=1000,T=1,alpha=2)

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