{
  "id": "1406.5484",
  "version": "v2",
  "published": "2014-06-20T18:42:18.000Z",
  "updated": "2015-03-05T09:29:12.000Z",
  "title": "Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry",
  "authors": [
    "Laurent Decreusefond",
    "Matthias Schulte",
    "Christoph Thaele"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "A Poisson or a binomial process on an abstract state space and a symmetric function $f$ acting on $k$-tuples of its points are considered. They induce a point process on the target space of $f$. The main result is a functional limit theorem which provides an upper bound for an optimal transportation distance between the image process and a Poisson process on the target space. The technical background are a version of Stein's method for Poisson process approximation, a Glauber dynamics representation for the Poisson process and the Malliavin formalism. As applications of the main result, error bounds for approximations of U-statistics by Poisson, compound Poisson and stable random variables are derived and examples from stochastic geometry are investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-20T18:42:18.000Z",
      "title": "Functional Poisson approximation in Rubinstein distance",
      "abstract": "A Poisson or a binomial process on an abstract state space and a symmetric function $f$ acting on $k$-tuples of its points are considered. They induce a point process on the target space of $f$. The main result is a functional limit theorem which provides an upper bound for an optimal transportation distance between the image process and a Poisson process on the target space. The technical background are a version of Stein's method for Poisson process approximation, a Glauber dynamic representation for the Poisson process and the Malliavin formalism. As applications of the main result, error bounds for approximations of U-statistics by Poisson, compound Poisson and stable random variables are derived and examples from stochastic geometry are investigated.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-05T09:29:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17",
      "60G55",
      "60D05",
      "60E07",
      "60H07"
    ],
    "keywords": [
      "functional poisson approximation",
      "rubinstein distance",
      "target space",
      "main result",
      "functional limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.5484D"
    }
  }
}