CONVERGENCE OF TIME-INHOMOGENEOUS GEODESIC RANDOM WALKS AND ITS APPLICATION TO COUPLING METHODS

• 成果类型: Article
• 署名作者: Kuwada, Kazumasa
• 署名单位: Ochanomizu University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP676
• 发表日期: 2012
• 页码: 1945-1979
• 关键词: Manifolds; THEOREM

摘要

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.