# Stochastic differential of a particular martingale

1. Oct 13, 2011

### steve1985

Hello everyone,
I'm studying from Oksendal's book, and I'm stuck at an excercise which asks you to find the differential form of:

X(t) = (W(t)$^{2}$-t)$^{2}$ - 4$\int$ (W(s))$^{2}$ds
where W(t) is a Brownian Motion.

I tried several possible functions g(t,W(t)) which could have led to a potential solution (by finding d(g(t,W(t))) with Ito), but none led me any closer to a solution.

Can you please put me in the right direction?

thanks!
Steve

PS. I posted this in the wrong place, it should have been in "Homeworks and coursework questions", but I don't know how to move it...

Last edited: Oct 13, 2011
2. Oct 15, 2011

### bpet

Yes Ito's formula only applies to the first term in the sum. For the second term, if the integral is from 0 to t, just apply the stochastic version of the fundamental law of calculus.