On the exit distribution of partially reflected Brownian motion in planar domains

TL;DR

This paper investigates the exit distribution of planar partially reflected Brownian motion, demonstrating that its dimension can be made arbitrarily close to 2, which has implications for understanding boundary behaviors in stochastic processes.

Contribution

It establishes that the dimension of the exit distribution for partially reflected Brownian motion in planar domains can approach 2, revealing new insights into boundary phenomena.

Findings

Exit distribution dimension can be arbitrarily close to 2

Provides new understanding of boundary behavior in stochastic processes

Advances theoretical knowledge of reflected Brownian motion

Abstract

We show that the dimension of the exit distribution of planar partially reflected Brownian motion can be arbitrarily close to 2.