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

Published online by Cambridge University Press:  23 November 2020

Maher Boudabra  and
Greg Markowsky
Maher Boudabra*
Affiliation:
Monash University
Greg Markowsky*
Affiliation:
Monash University
*
*Postal address: Clayton, Victoria, Australia.
*Postal address: Clayton, Victoria, Australia.
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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.

Keywords

Planar Brownian motionexit time
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1135 - 1149
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Copyright
© Applied Probability Trust 2020

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