{
  "id": "1002.0224",
  "version": "v1",
  "published": "2010-02-01T10:45:39.000Z",
  "updated": "2010-02-01T10:45:39.000Z",
  "title": "Convergence of U-statistics for interacting particle systems",
  "authors": [
    "P. Del Moral",
    "F. Patras",
    "S. Rubenthaler"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, de99]. When dealing with Feynman-Kac and other interacting particle systems of Monte Carlo type, one faces a new type of problem. Namely, in a sample of N particles obtained through the corresponding algorithms, the distributions of the particles are correlated -although any finite number of them is asymptotically independent with respect to the total number N of particles. In the present article, exploiting the fine asymptotics of particle systems, we prove convergence theorems for U-statistics in this framework.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-01T10:45:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C22",
      "62E20",
      "60F05"
    ],
    "keywords": [
      "interacting particle systems",
      "u-statistics",
      "monte carlo type",
      "convergence theorems",
      "independence assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.0224D"
    }
  }
}