What is the covariance function for $U(t)$ if $U(t) = e^{-t}B(e^{2t})$ for $t \geq 0$ where $B(t)$ is standard Brownian motion? Any help would be great
Covariance of Brownian Motion
0
$\begingroup$
stochastic-processes
-
1Do you know that ${\rm Cov}(B(s),B(t))=s$ for $0 \leq s \leq t$? – 2011-04-27
1 Answers
1
Hint: consider $\min\{e^{2s},e^{2t}\}$ for $0 \leq s \leq t$.