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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

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    The process $U$ is a standard OU process.2011-04-27
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    See also the answer in http://math.stackexchange.com/questions/30817/covariance-function-for-brownian-motion/30837#30837.2011-04-27
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    Do you know that ${\rm Cov}(B(s),B(t))=s$ for $0 \leq s \leq t$?2011-04-27

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Hint: consider $\min\{e^{2s},e^{2t}\}$ for $0 \leq s \leq t$.