3.3. Let B(t) be a standard Brownian motion. Show that B(u) - uB(1), 0 < u <...

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3.3. Let B(t) be a standard Brownian motion. Show that B(u) - uB(1), 0 < u < 1, is independent of B(1).

(a) Use this to show that B°(t) = B(t) - tB(1), 0 s t < 1, is a Brownian bridge.

(b) Use the representation in

(a) to evaluate the covariance function for a Brownian bridge.

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An Introduction To Stochastic Modeling

ISBN: 9780126848878

3rd Edition

Authors: Samuel Karlin, Howard M. Taylor

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Question Posted: Oct 31, 2024 06:00 AM

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3.3. Let B(t) be a standard Brownian motion. Show that B(u) - uB(1), 0 < u <...

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An Introduction To Stochastic Modeling

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