{
  "id": "math/0511052",
  "version": "v1",
  "published": "2005-11-02T16:24:46.000Z",
  "updated": "2005-11-02T16:24:46.000Z",
  "title": "Asymptotic properties of power variations of Lévy processes",
  "authors": [
    "Jean Jacod"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\\'{e}vy process. One can completely elucidate the first order behavior (convergence in probability, possibly after normalization). As for the associated CLT, one can show some versions of it, but only in a limited number of cases. In some other cases, a CLT just does not exist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-02T16:24:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lévy processes",
      "asymptotic properties",
      "first order behavior",
      "asymptotic behavior",
      "realized power variations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11052J"
    }
  }
}