Volume growth, Comparison theorem and Escape Rate of Diffusion Process

2013/10/15 by Shun-Xiang Ouyang, Shunxiang Ouyang, Ouyang, Shunxiang · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Biology Tumor Growth #Stochastic processes and statistical mechanics #math.PR #msc:31C25 #msc:58J65 #msc:60J60

paper · pdf · doi:10.48550/arxiv.1310.3996

25 pages

arxiv created 2013/10/15 · arxiv updated 2013/10/16

Abstract

We study the escape rate of diffusion process with two approaches. We first give an upper rate function for the diffusion process associated with a symmetric, strongly local regular Dirichlet form. The upper rate function is in terms of the volume growth of the underlying state space. The method is due to Hsu and Qin [Ann. Probab., 38(4), 2010] where an upper rate function was given for Brownian motion on Riemannian manifold. In the second part, we prove a comparison theorem and give an upper rate function for diffusion process on Riemannian manifold in terms of the upper rate function for the solution process of a one dimensional stochastic differential equation.

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