On pathwise uniqueness for reflecting Brownian motion in $C^{1+\gamma}$ domains

TL;DR

This paper proves pathwise uniqueness for reflecting Brownian motion in domains with $C^{1+ ext{gamma}}$ regularity when gamma exceeds 1/2 in dimensions three and higher.

Contribution

It establishes the pathwise uniqueness for reflecting Brownian motion in $C^{1+ ext{gamma}}$ domains with gamma > 1/2, extending previous results to higher dimensions.

Findings

Pathwise uniqueness holds in $C^{1+ ext{gamma}}$ domains for gamma > 1/2.

Results apply to dimensions $d \,\geq\, 3$.

Advances understanding of stochastic differential equations with reflection.

Abstract

Pathwise uniqueness holds for the Skorokhod stochastic differential equation in $C^{1+\gamma}$ domains in $\mathbb{R}^d$ for $\gamma >1/2$ and $d\geq3$.