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2006 Synchronous couplings of reflected Brownian motions in smooth domains
Krzysztof Burdzy, Zhen-Qing Chen, Peter Jones
Illinois J. Math. 50(1-4): 189-268 (2006). DOI: 10.1215/ijm/1258059475

Abstract

For every bounded planar domain $D$ with a smooth boundary, we define a ``Lyapunov exponent'' $\Lambda(D)$ using a fairly explicit formula. We consider two reflected Brownian motions in $D$, driven by the same Brownian motion (i.e., a ``synchronous coupling''). If $\Lambda(D)>0$ then the distance between the two Brownian particles goes to $0$ exponentially fast with rate $\Lambda (D)/(2|D|)$ as time goes to infinity. The exponent $\Lambda(D)$ is strictly positive if the domain has at most one hole. It is an open problem whether there exists a domain with $\Lambda(D)<0$.

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Krzysztof Burdzy. Zhen-Qing Chen. Peter Jones. "Synchronous couplings of reflected Brownian motions in smooth domains." Illinois J. Math. 50 (1-4) 189 - 268, 2006. https://doi.org/10.1215/ijm/1258059475

Information

Published: 2006
First available in Project Euclid: 12 November 2009

zbMATH: 1142.60053
MathSciNet: MR2247829
Digital Object Identifier: 10.1215/ijm/1258059475

Subjects:
Primary: 60J65

Rights: Copyright © 2006 University of Illinois at Urbana-Champaign

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Vol.50 • No. 1-4 • 2006
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