A boundary Harnack principle and its application to analyticity of 3D Brownian intersection exponents

TL;DR

This paper proves that domains in three-dimensional space with Brownian motion traces satisfy the boundary Harnack principle and uses this to establish the analyticity of 3D Brownian intersection exponents.

Contribution

It establishes the boundary Harnack principle for domains in 3D with Brownian traces and proves the analyticity of intersection exponents, advancing understanding of Brownian motion properties.

Findings

Domains with Brownian traces satisfy BHP almost surely

Intersection exponents for 3D Brownian motion are analytic

Provides new tools for studying Brownian motion in 3D

Abstract

We show that a domain in $\mathbb{R}^3$ with the trace of a 3D Brownian motion removed almost surely satisfies the boundary Harnack principle (BHP). Then, we use it to prove that the intersection exponents for 3D Brownian motion are analytic.