{
  "id": "0908.4222",
  "version": "v2",
  "published": "2009-08-28T14:58:57.000Z",
  "updated": "2009-11-13T15:37:33.000Z",
  "title": "Stochastic completeness and volume growth",
  "authors": [
    "Christian Baer",
    "G. Pacelli Bessa"
  ],
  "comment": "11 pages, 5 figures, published version",
  "journal": "Proc. Amer. Math. Soc. 138 (2010), 2629-2640",
  "doi": "10.1090/S0002-9939-10-10281-0",
  "categories": [
    "math.DG",
    "math.PR"
  ],
  "abstract": "It has been suggested in 1999 that a certain volume growth condition for geodesically complete Riemannian manifolds might imply that the manifold is stochastically complete. This is motivated by a large class of examples and by a known analogous criterion for recurrence of Brownian motion. We show that the suggested implication is not true in general. We also give counter-examples to a converse implication.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-11-13T15:37:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J35",
      "58J65"
    ],
    "keywords": [
      "stochastic completeness",
      "volume growth condition",
      "geodesically complete riemannian manifolds",
      "brownian motion",
      "converse implication"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.4222B"
    }
  }
}