{
  "id": "0910.1996",
  "version": "v1",
  "published": "2009-10-12T19:15:38.000Z",
  "updated": "2009-10-12T19:15:38.000Z",
  "title": "Cumulants on the Wiener Space",
  "authors": [
    "Ivan Nourdin",
    "Giovanni Peccati"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We combine infinite-dimensional integration by parts procedures with a recursive relation on moments (reminiscent of a formula by Barbour (1986)), and deduce explicit expressions for cumulants of functionals of a general Gaussian field. These findings yield a compact formula for cumulants on a fixed Wiener chaos, virtually replacing the usual \"graph/diagram computations\" adopted in most of the probabilistic literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-12T19:15:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G15",
      "60H05",
      "60H07"
    ],
    "keywords": [
      "wiener space",
      "general gaussian field",
      "deduce explicit expressions",
      "parts procedures",
      "infinite-dimensional integration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.1996N"
    }
  }
}