Exercises 2.3 Wick's identity Let Wt be a Brownian motion. 1. Prove that EP[eiuWt ] = e????u2t
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Exercises 2.3 Wick's identity Let Wt be a Brownian motion.
1. Prove that EP[eiuWt ] = e????u2t 2
2. Deduce the following formula, called the Wick identity, 8n 2 N EP[(Wt)2n] =
(2n ???? 1)!
2n????1(n ???? 1)! tn EP[(Wt)2n+1] = 0
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