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Chapter 7 stochastic differential equation

M

mugono

Ton up Member
In the example given on page 21 I have obtained a slightly different solution to the one given.

For convenience, I repeat the question here:

A process X_t satisfies the stochastic differential equation:

dX_t = sigma(X_t)dB_t + mu(X_t)dt

Deduce the stochastic differential equation for the process X_t^3

The solution given is

d(Xt^3) = 3Xt^2*sigma(Xt)dB_t + [3Xt^2*mu(Xt) + 3Xt*sigma^2(Xt)]dt

My solution is:

d(Xt^3) = 3Xt^2*sigma(Xt)dB_t + [3Xt^2*mu(Xt) + 3Xt]dt

I've double checked my workings for any obvious mistakes but haven't found one. Is the solution given in the notes wrong?

Any help would be much appreciated.

Thanks.
 
Stochastic calculus and Ito processes

My answer was incorrect I've just seen. The solution given is correct.
 
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