Volume Growth and Escape Rate of Brownian Motion on a Complete Riemannian Manifold

  • GUANGNAN QIN A BSTRACT
  • Published 2009

Abstract

We give an effective escape rate function for Brownian motion on a complete Riemannian manifold in terms of the volume growth function of the manifold. An important step in the work is estimating small tail probabilities of crossing times between concentric geodesic spheres by reflecting Brownian motions on geodesic balls. 

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