{
  "id": "2005.11121",
  "version": "v1",
  "published": "2020-05-22T12:01:42.000Z",
  "updated": "2020-05-22T12:01:42.000Z",
  "title": "Strong renewal theorem and local limit theorem in the absence of regular variation",
  "authors": [
    "Peter Kevei",
    "Dalia Terhesiu"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We obtain a strong renewal theorem with infinite mean beyond regular variation, when the underlying distribution belongs to the domain of geometric partial attraction a semistable law with index $\\alpha\\in (1/2,1]$. In the process we obtain local limit theorems for both finite and infinite mean, that is for the whole range $\\alpha\\in (0,2)$. We also derive the aymptotics of the renewal function for $\\alpha\\in (0,1]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-22T12:01:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K05"
    ],
    "keywords": [
      "local limit theorem",
      "strong renewal theorem",
      "regular variation",
      "infinite mean",
      "geometric partial attraction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}