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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
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.
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- © Applied Probability Trust 2020
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