{
  "id": "1008.1701",
  "version": "v1",
  "published": "2010-08-10T12:15:38.000Z",
  "updated": "2010-08-10T12:15:38.000Z",
  "title": "An elementary approach to Brownian local time based on simple, symmetric random walks",
  "authors": [
    "Tamas Szabados",
    "Balazs Szekely"
  ],
  "comment": "17 pages",
  "journal": "Periodica Mathematica Hungarica, Volume 51, Number 1, Pages 79-98, (2005)",
  "doi": "10.1007/s10998-005-0022-8",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we define Brownian local time as the almost sure limit of the local times of a nested sequence of simple, symmetric random walks. The limit is jointly continuous in $(t,x)$. The rate of convergence is $n^{\\frac14} (\\log n)^{\\frac34}$ that is close to the best possible. The tools we apply are almost exclusively from elementary probability theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-10T12:15:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J55",
      "60J65",
      "60F15"
    ],
    "keywords": [
      "symmetric random walks",
      "elementary approach",
      "define brownian local time",
      "elementary probability theory",
      "sure limit"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.1701S"
    }
  }
}