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An Arctangent Law

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 $M_r$.

3 nodes2 linksoverview previewAn Arctangent Law
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An Arctangent Law3 visible / 3 total nodes / 2 links
AuthorshipTopic signalWAn Arctangent Lawpreprint / 2016AVassilis G. PapanicolaouResearcherTmath.PR7239 works
PaperSignal 102 links

An Arctangent Law

preprint / 2016

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