{
  "id": "0811.4485",
  "version": "v2",
  "published": "2008-11-27T08:40:41.000Z",
  "updated": "2010-02-12T07:26:50.000Z",
  "title": "Second order Poincaré inequalities and CLTs on Wiener space",
  "authors": [
    "Ivan Nourdin",
    "Giovanni Peccati",
    "Gesine Reinert"
  ],
  "comment": "16 pages. A typo in the statement of Theorem 1.1 has been corrected",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove infinite-dimensional second order Poincar\\'e inequalities on Wiener space, thus closing a circle of ideas linking limit theorems for functionals of Gaussian fields, Stein's method and Malliavin calculus. We provide two applications: (i) to a new \"second order\" characterization of CLTs on a fixed Wiener chaos, and (ii) to linear functionals of Gaussian-subordinated fields.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-02-12T07:26:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G15",
      "60H07"
    ],
    "keywords": [
      "wiener space",
      "infinite-dimensional second order poincare inequalities",
      "ideas linking limit theorems",
      "linear functionals",
      "gaussian fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.4485N"
    }
  }
}