{
  "id": "math/0610056",
  "version": "v1",
  "published": "2006-10-02T02:35:08.000Z",
  "updated": "2006-10-02T02:35:08.000Z",
  "title": "A note on recurrent random walks",
  "authors": [
    "Dimitrios Cheliotis"
  ],
  "comment": "8 pages",
  "journal": "Statistics and Probability Letters 76 (2006) 1025-1031",
  "categories": [
    "math.PR"
  ],
  "abstract": "For any recurrent random walk (S_n)_{n>0} on R, there are increasing sequences (g_n)_{n>0} converging to infinity for which (g_n S_n)_{n>0} has at least one finite accumulation point. For one class of random walks, we give a criterion on (g_n)_{n>0} and the distribution of S_1 determining the set of accumulation points for (g_n S_n)_{n>0}. This extends, with a simpler proof, a result of K.L. Chung and P. Erdos. Finally, for recurrent, symmetric random walks, we give a criterion characterizing the increasing sequences (g_n)_{n>0} of positive numbers for which liminf g_n|S_n|=0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-02T02:35:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F99"
    ],
    "keywords": [
      "recurrent random walk",
      "increasing sequences",
      "symmetric random walks",
      "finite accumulation point",
      "simpler proof"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10056C"
    }
  }
}