{
  "id": "math/0501182",
  "version": "v1",
  "published": "2005-01-12T12:20:48.000Z",
  "updated": "2005-01-12T12:20:48.000Z",
  "title": "Tanaka formula for symmetric Lévy processes",
  "authors": [
    "Paavo Salminen",
    "Marc Yor"
  ],
  "comment": "24 pages, no figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "Starting from the potential theoretic definition of the local times of a Markov process - when these exist - we obtain a Tanaka formula for the local times of symmetric L\\'{e}vy processes. The most interesting case is that of the symmetric $\\al$-stable L\\'{e}vy process (for $\\al\\in[1,2]$) which is studied in detail. In particular, we determine which powers of such a process are semimartingales. These results complete, in a sense, the works by K. Yamada \\cite{yamada02} and Fitzsimmons and Getoor \\cite{fitzsimmonsgetoor92a}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-12T12:20:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60J60",
      "60J70"
    ],
    "keywords": [
      "symmetric lévy processes",
      "tanaka formula",
      "local times",
      "potential theoretic definition",
      "results complete"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1182S"
    }
  }
}