{
  "id": "1010.3596",
  "version": "v1",
  "published": "2010-10-18T13:34:12.000Z",
  "updated": "2010-10-18T13:34:12.000Z",
  "title": "Volume growth and escape rate of Brownian motion on a complete Riemannian manifold",
  "authors": [
    "Elton P. Hsu",
    "Guangnan Qin"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AOP519 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2010, Vol. 38, No. 4, 1570-1582",
  "doi": "10.1214/09-AOP519",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give an effective upper escape rate function for Brownian motion on a complete Riemannian manifold in terms of the volume growth of the manifold. An important step in the work is estimating the small tail probability of the crossing time between two concentric geodesic spheres by reflecting Brownian motions on the larger geodesic ball.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-18T13:34:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete riemannian manifold",
      "brownian motion",
      "volume growth",
      "effective upper escape rate function",
      "small tail probability"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.3596H"
    }
  }
}