{
  "id": "1306.2674",
  "version": "v1",
  "published": "2013-06-11T23:16:34.000Z",
  "updated": "2013-06-11T23:16:34.000Z",
  "title": "Convergence of the Fourth Moment and Infinite Divisibility",
  "authors": [
    "Octavio Arizmendi"
  ],
  "comment": "10 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note we prove that, for infinitely divisible laws, convergence of the fourth moment to 3 is sufficient to ensure convergence in law to the Gaussian distribution. Our results include infinitely divisible measures with respect to classical, free, Boolean and monotone convolution. A similar criterion is proved for compound Poissons with jump distribution supported on a finite number of atoms. In particular, this generalizes recent results of Nourdin and Poly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-11T23:16:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L54",
      "46L50",
      "60E07"
    ],
    "keywords": [
      "fourth moment",
      "infinite divisibility",
      "finite number",
      "ensure convergence",
      "monotone convolution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.2674A"
    }
  }
}