{
  "id": "1209.2069",
  "version": "v2",
  "published": "2012-09-10T17:30:45.000Z",
  "updated": "2012-11-06T14:16:28.000Z",
  "title": "A note on the volume growth criterion for stochastic completeness of weighted graphs",
  "authors": [
    "Xueping Huang"
  ],
  "comment": "23 pages",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We generalize the weak Omori-Yau maximum principle to the setting of strongly local Dirichlet forms. As an application, we obtain an analytic approach to compare the stochastic completeness of a weighted graph with that of an associated metric graph. This comparison result played an essential role in the volume growth criterion of Folz \\cite{FOLZSC}, who first proved it via a probabilistic approach. We also give an alternative analytic proof based on a criterion in Fukushima, Oshima, and Takeda \\cite{FOT}.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-06T14:16:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C81",
      "60J27"
    ],
    "keywords": [
      "volume growth criterion",
      "stochastic completeness",
      "weighted graph",
      "weak omori-yau maximum principle",
      "strongly local dirichlet forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2069H"
    }
  }
}