By Feng-Yu Wang

Stochastic research on Riemannian manifolds with no boundary has been good demonstrated. although, the research for reflecting diffusion procedures and sub-elliptic diffusion strategies is way from whole. This publication comprises contemporary advances during this course in addition to new rules and effective arguments, that are the most important for extra advancements. Many effects contained the following (for instance, the formulation of the curvature utilizing derivatives of the semigroup) are new between current monographs even within the case with no boundary.

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