Problem 3. Let f € C(R) and X, := S f(s)dB, for t > 0, where {B;}s>0 denotes a Brownian motion. (a) Prove from first pri

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Problem 3 Let F C R And X S F S Db For T 0 Where B S 0 Denotes A Brownian Motion A Prove From First Pri 1 (25.28 KiB) Viewed 15 times

Problem 3. Let f € C(R) and X, := S f(s)dB, for t > 0, where {B;}s>0 denotes a Brownian motion. (a) Prove from first principles (without using Ito's Lemma) that {X2}t>o has the quadratic variation XX, (in mean square). (b) Show that {X2}ezo is a Brownian martingale. (c) Show that the stochastic process {Y{}t>o, defined for t > 0 by Y = B - 3B, is a Brownian martingale. (X,X) = ["f(s)?ds