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December 18th, 2016, 03:45 AM   #1
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From: london

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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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