Maximizing the $p$-th moment of exit time of planar Brownian motion from a given domain
Probability
2020-01-24 v1 Complex Variables
Abstract
In this paper we address the question of finding the point which maximizes the -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.
Keywords
Cite
@article{arxiv.2001.08330,
title = {Maximizing the $p$-th moment of exit time of planar Brownian motion from a given domain},
author = {Maher Boudabra and Greg Markowsky},
journal= {arXiv preprint arXiv:2001.08330},
year = {2020}
}