Maximizing the pth moment of the exit time of planar Brownian motion from a given domain

Maher Boudabra, Greg Markowsky

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Abstract

In this paper we address the question of finding the point which maximizes the pth moment of the exit time of planar Brownian motion from a given domain. We present a geometrical method for excluding parts of the domain from consideration which makes use of a coupling argument and the conformal invariance of Brownian motion. In many cases the maximizing point can be localized to a relatively small region. Several illustrative examples are presented.

Original languageEnglish
Pages (from-to)1135-1149
Number of pages15
JournalJournal of Applied Probability
Volume57
Issue number4
DOIs
Publication statusPublished - Dec 2020

Keywords

  • exit time
  • Planar Brownian motion

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