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MGF for two correlated wiener processes

Heads-up this forms part of an assignment question so I'm really just looking for a foothold on how to go about solving it.

Given two standard Brownian Motions such that http://latex.codecogs.com/png.latex?...ce;\ne&space;0

Find the MGF: http://latex.codecogs.com/png.latex?...pace;<&space;t

My thoughts...

I know the distribution for Bt & Ws, so my first thought is to at least define the double integral (based on the joint pdf for a bivariate normal distribution, given I know the mean/var for both the Bt & Ws processes, as well as their correlation coeff.). I can then try to solve that

Is there an alternate/more-sane approach? Perhaps involving application of Ito's Lemma/stoch.calc rules?

Help gratefully received

Re: MGF for two correlated wiener processes

Hey MathCrash.

I think you should do it the way you intended. There are results for MGF's involving multi-variate normal distributions which means if you get stuck, just look it up and follow the proof of how the results were obtained.