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Solve this quesiton by steps, thank you BM-standard Brownian motion, GP-Gaussian process H4 Let o, u E R and of > 0 be fixed parameters.

Solve this quesiton by steps, thank you

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BM-standard Brownian motion, GP-Gaussian process H4 Let o, u E R and of > 0 be fixed parameters. Assume (B.) is standard Brownian motion, and let (Wt) a Brownian motion We := ut + oB, with linear drift, t 2 0. If x / 0, set TW = inf {t c [0, co) : We = x} to be the first time that We hits the level x. (a) Show that (exW.) is a martingale if and only if a = 0 or o = -2p/02. (b) Let a TW ) e-2ub/02 - e-2pa/02

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