Unformatted text preview: X with ﬁnite expectation, it holds that E { XY G} = Y E { X G} . 5) Let { B t : t ≥ } be a Brownian motion, and {F B t } t ≥ be the ﬁltration generated by B . Using the deﬁnition of a Brownian motion to verify that B is indeed an {F B t }martingale. 6) Suppose that { B t : t ≥ } is a standard Brownian motion. Show that for any constant c > 0, the scaled process W t := √ cB t/c , t ≥ 0 is also a standard Brownian motion. 7) Let σ , τ be two stopping times, show that both σ ∧ τ and σ ∨ τ are also stopping times. 1...
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 Fall '09
 MAJIN
 Variance, Brownian Motion, Probability theory, standard Brownian motion

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