{
  "id": "1301.7289",
  "version": "v1",
  "published": "2013-01-30T17:04:32.000Z",
  "updated": "2013-01-30T17:04:32.000Z",
  "title": "Gamma limits and U-statistics on the Poisson space",
  "authors": [
    "Giovanni Peccati",
    "Christoph Thaele"
  ],
  "journal": "ALEA 10, 525-560 (2013)",
  "categories": [
    "math.PR"
  ],
  "abstract": "Using Stein's method and the Malliavin calculus of variations, we derive explicit estimates for the Gamma approximation of functionals of a Poisson measure. In particular, conditions are presented under which the distribution of a sequence of multiple Wiener-Ito stochastic integrals with respect to a compensated Poisson measure converges to a Gamma distribution. As an illustration, we present a quantitative version and a non-central extension of a classical theorem by de Jong in the case of degenerate U-statistics of order two. Several multidimensional extensions, in particular allowing for mixed or hybrid limit theorems, are also provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-30T17:04:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G55",
      "60H05",
      "60H07",
      "62E20"
    ],
    "keywords": [
      "poisson space",
      "gamma limits",
      "multiple wiener-ito stochastic integrals",
      "compensated poisson measure converges",
      "hybrid limit theorems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.7289P"
    }
  }
}