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arXiv · 1602.05500

An Arctangent Law

Vassilis G. Papanicolaou
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Abstract

Let $M_r$ be the maximum value of an one-dimensional Brownian motion on the (time) interval $[0, r]$. We derive an explicit formula for the distribution of the time required (after $r$) for the Brownian motion to exceed $M_r$.

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Vassilis G. Papanicolaou. 2016-02-16. An Arctangent Law. https://arxiv.org/abs/1602.05500

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