{
  "id": "1205.3033",
  "version": "v3",
  "published": "2012-05-14T14:09:06.000Z",
  "updated": "2014-04-03T15:34:59.000Z",
  "title": "Moments and central limit theorems for some multivariate Poisson functionals",
  "authors": [
    "Guenter Last",
    "Mathew D. Penrose",
    "Matthias Schulte",
    "Christoph Thaele"
  ],
  "journal": "Adv. Appl. Probab. 46, 348-364 (2014)",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\\^o integrals with respect to the compensated Poisson process. Second, a multivariate central limit theorem is shown for a vector whose components admit a finite chaos expansion of the type of a Poisson U-statistic. The approach is based on recent results of Peccati et al.\\ combining Malliavin calculus and Stein's method, and also yields Berry-Esseen type bounds. As applications, moment formulae and central limit theorems for general geometric functionals of intersection processes associated with a stationary Poisson process of $k$-dimensional flats in $\\R^d$ are discussed.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-04-03T15:34:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "60H07",
      "60F05",
      "60G55"
    ],
    "keywords": [
      "multivariate poisson functionals",
      "multivariate central limit theorem",
      "yields berry-esseen type bounds",
      "general geometric functionals",
      "finite chaos expansion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.3033L"
    }
  }
}