On the Time for Brownian Motion to Visit Every Point on a Circle

Abstract

Consider a Wiener process $W$ on a circle of circumference $L$. We prove the rather surprising result that the Laplace transform of the distribution of the first time, ${\theta }_L$, when the Wiener process has visited every point of the circle can be solved in closed form using a continuous recurrence approach.

arXiv comment8 pages, 1 figure