Convergence of time-inhomogeneous geodesic random walks and its application to coupling methods

Kazumasa Kuwada

doi:10.1214/11-aop676

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arXiv · 1210.3138

Convergence of time-inhomogeneous geodesic random walks and its application to coupling methods

Kazumasa Kuwada

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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. 2012-10-11. Convergence of time-inhomogeneous geodesic random walks and its application to coupling methods. https://doi.org/10.1214/11-aop676

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