Mirror coupling of reflecting Brownian motion and an application to\n Chavel's conjecture

2010/04/14 by Mihai N. Pascu, Pascu, Mihai N. · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #60H20. Secondary 35K05 #60H30. #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 60J65 #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1004.2398

openalex publication_date 2010/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a series of papers, Burdzy et. al. introduced the \mirror coupling\nof reflecting Brownian motions in a smooth bounded domain D\⊂\n\ℝ^d, and used it to prove certain properties of eigenvalues and\neigenfunctions of the Neumann Laplaceian on D. In the present paper we show\nthat the construction of the mirror coupling can be extended to the case when\nthe two Brownian motions live in different domains D₁,D₂\⊂\n\ℝ^d. As an application of the construction, we derive a unifying\nproof of the two main results concerning the validity of Chavel's conjecture on\nthe domain monotonicity of the Neumann heat kernel, due to I. Chavel\n( citeChavel), respectively W. S. Kendall ( citeKendall).\n

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