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.
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
Find the MGF:
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
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.