English

An Arctangent Law

Probability 2016-02-18 v1

Abstract

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

Keywords

Cite

@article{arxiv.1602.05500,
  title  = {An Arctangent Law},
  author = {Vassilis G. Papanicolaou},
  journal= {arXiv preprint arXiv:1602.05500},
  year   = {2016}
}

Comments

3 pages

R2 v1 2026-06-22T12:52:23.609Z