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

Kazumasa Kuwada

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

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 timeinhomogeneous 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.

Original languageEnglish
Pages (from-to)1945-1979
Number of pages35
JournalAnnals of Probability
Volume40
Issue number5
DOIs
Publication statusPublished - 2012

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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