An Arctangent Law

2016/02/16 by Vassilis G. Papanicolaou, Papanicolaou, Vassilis G.
Mathematics · #60J65 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J65

paper · pdf · doi:10.48550/arxiv.1602.05500

3 pages

arxiv created 2016/02/16 · arxiv updated 2016/02/18

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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