Let W(t) be the standard Brownian motion, and let X(t) = t W(1/t) for t > 0, X(0) = 0. Show that the covariance (Cov) function of X(t) is the same as the covariance function of W(t): Cov(X(t); X(s)) = Cov(W(t); W(s)) for all s; t > 0. Assuming that the paths of X(t) are continuous with probability 1, argue that X(t) is standard Brownian motion?
Let W(t) be the standard Brownian motion, and let X(t) = t W(1/t) for t > 0, X(0) = 0. Show that the covariance (Cov) function of X(t) is the same as the covariance function of W(t): Cov(X(t); X(s)) = Cov(W(t); W(s)) for all s; t > 0. Assuming that the paths of X(t) are continuous with probability 1, argue that X(t) is standard Brownian motion?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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Let W(t) be the standard Brownian motion, and let X(t) = t W(1/t) for t > 0, X(0) = 0. Show that the
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