{
  "id": "1112.5070",
  "version": "v4",
  "published": "2011-12-21T15:59:48.000Z",
  "updated": "2014-02-25T11:30:48.000Z",
  "title": "Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws",
  "authors": [
    "Ivan Nourdin",
    "Jan Rosiński"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/12-AOP826 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2014, Vol. 42, No. 2, 497-526",
  "doi": "10.1214/12-AOP826",
  "categories": [
    "math.PR"
  ],
  "abstract": "We characterize the asymptotic independence between blocks consisting of multiple Wiener-It\\^{o} integrals. As a consequence of this characterization, we derive the celebrated fourth moment theorem of Nualart and Peccati, its multidimensional extension and other related results on the multivariate convergence of multiple Wiener-It\\^{o} integrals, that involve Gaussian and non Gaussian limits. We give applications to the study of the asymptotic behavior of functions of short and long-range dependent stationary Gaussian time series and establish the asymptotic independence for discrete non-Gaussian chaoses.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-02-25T11:30:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic independence",
      "resulting limit laws",
      "dependent stationary gaussian time series",
      "long-range dependent stationary gaussian time"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.5070N"
    }
  }
}