=+8. For standard Brownian motion Xt, show that the stochastic processes Yt = Xt and Yt =

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=+8. For standard Brownian motion Xt, show that the stochastic processes Yt = Xt and Yt = X2 t − t enjoy the martingale property E(Yt+s| Xr, r ∈ [0, t]) = Yt for s > 0. (Hint: Xt+s − Xt is independent of Xt and distributed as Xs.)

11.9 Problems 293

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Applied Probability

ISBN: 9781441971647

2nd Edition

Authors: Kenneth Lange

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=+8. For standard Brownian motion Xt, show that the stochastic processes Yt = Xt and Yt = X2 t t enjoy the martingale property E(Yt+s| Xr, r [0, t]) = Yt for s > 0. (Hint: Xt+s Xt is independent...
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=+8. For standard Brownian motion Xt, show that the stochastic processes Yt = Xt and Yt =

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Applied Probability

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