Volume growth, Comparison theorem and Escape Rate of Diffusion Process

Shunxiang Ouyang

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arXiv · 1310.3996

Volume growth, Comparison theorem and Escape Rate of Diffusion Process

Shunxiang Ouyang

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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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Shunxiang Ouyang. 2013-10-15. Volume growth, Comparison theorem and Escape Rate of Diffusion Process. https://arxiv.org/abs/1310.3996

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