{
  "id": "1507.06790",
  "version": "v1",
  "published": "2015-07-24T09:30:09.000Z",
  "updated": "2015-07-24T09:30:09.000Z",
  "title": "The strong renewal theorem with infinite mean via local large deviations",
  "authors": [
    "R. A. Doney"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "A necessary and sufficient condition is established for an asymptotically stable random walk to satisfy the strong renewal theorem. This result is valid for all alpha in (0, 1), thus completing a result for alpha in (1/2, 1) which was proved in the 1963 paper of Garsia and Lamperti [6].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-24T09:30:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K05",
      "60F10"
    ],
    "keywords": [
      "strong renewal theorem",
      "local large deviations",
      "infinite mean",
      "sufficient condition",
      "asymptotically stable random walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150706790D"
    }
  }
}