Advanced Studies in Pure Mathematics

Couplings of the Brownian motion via discrete approximation under lower Ricci curvature bounds

Kazumasa Kuwada

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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.

Article information

Source
Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 273-292

Dates
Received: 12 January 2009
Revised: 9 April 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543086324

Digital Object Identifier
doi:10.2969/aspm/05710273

Mathematical Reviews number (MathSciNet)
MR2648265

Zentralblatt MATH identifier
1204.58031

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60H30: Applications of stochastic analysis (to PDE, etc.) 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]

Keywords
Coupling by reflection synchronous coupling Ricci curvature gradient estimate

Citation

Kuwada, Kazumasa. Couplings of the Brownian motion via discrete approximation under lower Ricci curvature bounds. Probabilistic Approach to Geometry, 273--292, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710273. https://projecteuclid.org/euclid.aspm/1543086324


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