Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
The process $U$ is a standard OU process. – Shai Covo Apr 27 '11 at 23:17
See also the answer in…. – Shai Covo Apr 27 '11 at 23:27
Do you know that ${\rm Cov}(B(s),B(t))=s$ for $0 \leq s \leq t$? – Shai Covo Apr 27 '11 at 23:42

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.