{
  "id": "1310.3996",
  "version": "v1",
  "published": "2013-10-15T10:37:04.000Z",
  "updated": "2013-10-15T10:37:04.000Z",
  "title": "Volume growth, Comparison theorem and Escape Rate of Diffusion Process",
  "authors": [
    "Shunxiang Ouyang"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-15T10:37:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J65",
      "60J60",
      "31C25"
    ],
    "keywords": [
      "upper rate function",
      "diffusion process",
      "escape rate",
      "volume growth",
      "comparison theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.3996O"
    }
  }
}