
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 18th, 2016, 02:45 AM  #1 
Senior Member Joined: Feb 2015 From: london Posts: 121 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 $\displaystyle c ∈ C^n$ 

Tags 
brownian, motion, multivariate 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Brownian Motion  mathmari  Advanced Statistics  0  April 28th, 2013 01:11 PM 
I got a Brownian motion problem  Mergh06  Advanced Statistics  0  October 11th, 2010 07:24 AM 
Independent Standard Brownian Motion Question  ocky  Advanced Statistics  0  October 17th, 2009 12:56 AM 
Brownian motion  elenaas  Advanced Statistics  7  September 26th, 2009 02:59 AM 
The Brownian motion and its relation to statisitics.  dk910  Algebra  0  December 8th, 2007 03:10 PM 