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math.PR2025
A method of solution for the inverse problem for -functions of planar Brownian motion
Greg Markowsky, Clayton McDonald
Given a planar domain , the harmonic measure distribution function , with base point , is the harmonic measure with pole at of the parts of the boundary which are…
math.PR2025
A collection of results relating the geometry of plane domains and the exit time of planar Brownian motion, II
Greg Markowsky, Clayton McDonald
This paper is the sequel to another with the same name (Buttigieg et al., Comput. Methods Funct. Theory, 2023), and is concerned with results of the same type. We deduce a result o…
math.PR2025
Stochastic Domination of Exit Times for Random Walks and Brownian Motion with Drift
Xi Geng, Greg Markowsky
In this note, by an elementary use of Girsanov's transform we show that the exit time for either a biased random walk or a drifted Brownian motion on a symmetric interval is stocha…