Boundary Trace of Reflecting Brownian Motions

2003/07/23 by Itaï Benjamini, Itai Benjamini, Benjamini, Itai +4 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.math/0307310

arxiv created 2003/07/23 · openalex publication_date 2003/07/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains is established. Exact Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are given. Extensions to stable-like jump processes and to symmetric reflecting diffusions are also mentioned.

Citations

• A new proof of Moser's parabolic harnack inequality using the old ideas of Nash

Cited by

• Sub-Gaussian heat kernel estimates for reflected diffusion on inner uniform domains

Related

• On trace of Brownian motion on the boundary of a strip
• Obliquely reflected Brownian motion in non-smooth planar domains
• Boundary trace theorems for symmetric reflected diffusions
• Heat kernel estimates for boundary traces of reflected diffusions on uniform domains
• Boundary Approximation for Sticky Jump-Reflected Processes on the Half-Line