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September 2012 Convergence of time-inhomogeneous geodesic random walks and its application to coupling methods
Kazumasa Kuwada
Ann. Probab. 40(5): 1945-1979 (September 2012). DOI: 10.1214/11-AOP676

Abstract

We study an approximation by time-discretized geodesic random walks of a diffusion process associated with a family of time-dependent metrics on manifolds. The condition we assume on the metrics is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow, and no further a priori curvature bound is required. As an application, we construct a coupling by reflection which yields a nice estimate of coupling time, and hence a gradient estimate for the associated semigroups.

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Kazumasa Kuwada. "Convergence of time-inhomogeneous geodesic random walks and its application to coupling methods." Ann. Probab. 40 (5) 1945 - 1979, September 2012. https://doi.org/10.1214/11-AOP676

Information

Published: September 2012
First available in Project Euclid: 8 October 2012

zbMATH: 1266.60060
MathSciNet: MR3025706
Digital Object Identifier: 10.1214/11-AOP676

Subjects:
Primary: 53C21 , 60F17
Secondary: 53C44 , 58J35 , 58J65

Keywords: coupling , diffusion process , Geodesic random walk , Ricci flow

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 5 • September 2012
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