The von Mises, or circular normal density on the unit circle is the hitting density of a two-dimensional Brownian motion starting at the origin, with constant drift velocity and direction. The concentration and location parameters of the density have a natural relation to the drift parameters.
"A Characterization of the Von Mises Distribution." Ann. Statist. 5 (4) 813 - 814, July, 1977. https://doi.org/10.1214/aos/1176343906