{
  "id": "1008.1006",
  "version": "v2",
  "published": "2010-08-05T15:40:21.000Z",
  "updated": "2011-03-02T10:54:42.000Z",
  "title": "Self-intersection local time of planar Brownian motion based on a strong approximation by random walks",
  "authors": [
    "Tamás Szabados"
  ],
  "comment": "36 pages. A new part on renormalized self-intersection local time has been added and several inaccuracies have been corrected. To appear in Journal of Theoretical Probability",
  "journal": "J. Theor. Probab. 25 (4), 1081-1118, 2012",
  "doi": "10.1007/s10959-011-0351-x",
  "categories": [
    "math.PR"
  ],
  "abstract": "The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka--Rosen--Yor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-02T10:54:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J55",
      "60F15",
      "60G50"
    ],
    "keywords": [
      "planar brownian motion",
      "planar self-intersection local time",
      "strong approximation",
      "random walk self-intersection local times",
      "simple random walk self-intersection local"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.1006S"
    }
  }
}