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?
2026-03-29 17:33:47.1774805627
Brownian motion on the circle
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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.