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?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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