Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $\mathbb S^1$ be the unit circle and $\Delta$ be the Laplace-Beltrami operator on $\mathbb S^1$ which is an infinitesimal generator of the correspondent Markov semigroup $P_t$. Is the explicit distribution of this Markov process known?

share|improve this question
You should check blms.oxfordjournals.org/content/28/6/643. –  Jon Dec 5 '11 at 15:16

1 Answer 1

up vote 3 down vote accepted

Brownian motion on the circle can be written as $X_t = e^{i B_t}$ where $B_t$ is a standard one-dimensional Brownian motion.

share|improve this answer
Thank a lot, Nate –  Ilya Dec 9 '11 at 15:44

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.