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arXiv · 1312.4632

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

Philip Ernst·Larry Shepp
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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.

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Philip Ernst, Larry Shepp. 2013-12-17. On the Time for Brownian Motion to Visit Every Point on a Circle. https://arxiv.org/abs/1312.4632

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