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VOL. 57 | 2010 Couplings of the Brownian motion via discrete approximation under lower Ricci curvature bounds
Kazumasa Kuwada

Editor(s) Motoko Kotani, Masanori Hino, Takashi Kumagai

Abstract

Along an idea of von Renesse, couplings of the Brownian motion on a Riemannian manifold and their extensions are studied. We construct couplings as a limit of coupled geodesic random walks whose components approximate the Brownian motion respectively. We recover Kendall and Cranston's result under lower Ricci curvature bounds instead of sectional curvature bounds imposed by von Renesse. Our method provides applications of coupling methods on spaces admitting a sort of singularity.

Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1204.58031
MathSciNet: MR2648265

Digital Object Identifier: 10.2969/aspm/05710273

Subjects:
Primary: 58J65, 60D05, 60H30

Rights: Copyright © 2010 Mathematical Society of Japan

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