{
  "id": "0912.1561",
  "version": "v1",
  "published": "2009-12-08T18:27:32.000Z",
  "updated": "2009-12-08T18:27:32.000Z",
  "title": "Explicit Conditions for the Convergence of Point Processes Associated to Stationary Arrays",
  "authors": [
    "Raluca Balan",
    "Sana Louhichi"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we consider a stationary array $(X_{j,n})_{1 \\leq j \\leq n, n \\geq 1}$ of random variables with values in $\\bR \\verb2\\2 \\{0\\}$ (which satisfy some asymptotic dependence conditions), and the corresponding sequence $(N_{n})_{n\\geq 1}$ of point processes, where $N_{n}$ has the points $X_{j,n}, 1\\leq j \\leq n$. Our main result identifies some explicit conditions for the convergence of the sequence $(N_{n})_{n \\geq 1}$, in terms of the probabilistic behavior of the variables in the array.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-08T18:27:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E07",
      "60G10"
    ],
    "keywords": [
      "point processes",
      "explicit conditions",
      "stationary array",
      "convergence",
      "asymptotic dependence conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1561B"
    }
  }
}