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December 18th, 2016, 03:45 AM  #1 
Senior Member Joined: Feb 2015 From: london Posts: 101 Thanks: 0  Multivariate Brownian motion
Let $\displaystyle Wt ∈ R^n$ be a multivariate Brownian motion whose components $\displaystyle W_{1,t},...,W_{n,t}$ satisfy $\displaystyle dW_{j,t}dW_{k,t} = δ_{jk}dt,$ 1 ≤ j,k ≤ n. I am trying to prove the following, however I dont really know where to start. Please could someone point me in the right direction $\displaystyle E[e^{c^T W_t}] = e^{\frac{t}{2}c^{2}}$, for any constant complex vector $\displaystyle c ∈ C^n$ 

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brownian, motion, multivariate 
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