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math.PR2024
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.PR2024
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…
math.PR2024
On the exponential integrability of the derivative of intersection and self-intersection local time for Brownian motion and related processes
Kaustav Das, Greg Markowsky, Binghao Wu
We show that the derivative of the intersection and self-intersection local times of alpha-stable processes are exponentially integrable for certain parameter values. This includes…