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

preprint2016arXivOpen access

Abstract

Consider a Wiener process WW on a circle of circumference LL. We prove the rather surprising result that the Laplace transform of the distribution of the first time, θLθ_L, when the Wiener process has visited every point of the circle can be solved in closed form using a continuous recurrence approach.

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