Maximizing the p-th moment of exit time of planar Brownian motion from a given domain

2020/01/23 by Boudabra, Maher, Markowsky, Greg · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2001.08330

Abstract

In this paper we address the question of finding the point which maximizes the p-th moment of the exit time of planar Brownian motion from a given domain. We present a geometrical method of 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.

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