Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 273 - 292
Couplings of the Brownian motion via discrete approximation under lower Ricci curvature bounds
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.
Received: 12 January 2009
Revised: 9 April 2009
First available in Project Euclid: 24 November 2018
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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]
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