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 language | English |
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Pages (from-to) | 1945-1979 |
Number of pages | 35 |
Journal | Annals of Probability |
Volume | 40 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2012 |
Externally published | Yes |
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty