{
  "id": "0709.3903",
  "version": "v3",
  "published": "2007-09-25T09:57:02.000Z",
  "updated": "2009-08-28T05:48:11.000Z",
  "title": "Noncentral convergence of multiple integrals",
  "authors": [
    "Ivan Nourdin",
    "Giovanni Peccati"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/08-AOP435 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2009, Vol. 37, No. 4, 1412-1426",
  "doi": "10.1214/08-AOP435",
  "categories": [
    "math.PR"
  ],
  "abstract": "Fix $\\nu>0$, denote by $G(\\nu/2)$ a Gamma random variable with parameter $\\nu/2$ and let $n\\geq2$ be a fixed even integer. Consider a sequence $\\{F_k\\}_{k\\geq1}$ of square integrable random variables belonging to the $n$th Wiener chaos of a given Gaussian process and with variance converging to $2\\nu$. As $k\\to\\infty$, we prove that $F_k$ converges in distribution to $2G(\\nu/2)-\\nu$ if and only if $E(F_k^4)-12E(F_k^3)\\to12\\nu^2-48\\nu$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-08-28T05:48:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G15",
      "60H05",
      "60H07"
    ],
    "keywords": [
      "multiple integrals",
      "noncentral convergence",
      "th wiener chaos",
      "square integrable random variables belonging",
      "gamma random"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.3903N"
    }
  }
}