{
  "id": "math/0701920",
  "version": "v3",
  "published": "2007-01-31T13:00:00.000Z",
  "updated": "2008-05-26T15:05:32.000Z",
  "title": "On lower limits and equivalences for distribution tails of randomly stopped sums",
  "authors": [
    "Denis Denisov",
    "Serguei Foss",
    "Dmitry Korshunov"
  ],
  "comment": "Published in at http://dx.doi.org/10.3150/07-BEJ111 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)",
  "journal": "Bernoulli 2008, Vol. 14, No. 2, 391-404",
  "doi": "10.3150/07-BEJ111",
  "categories": [
    "math.PR"
  ],
  "abstract": "For a distribution $F^{*\\tau}$ of a random sum $S_{\\tau}=\\xi_1+...+\\xi_{\\tau}$ of i.i.d. random variables with a common distribution $F$ on the half-line $[0,\\infty)$, we study the limits of the ratios of tails $\\bar{F^{*\\tau}}(x)/\\bar{F}(x)$ as $x\\to\\infty$ (here, $\\tau$ is a counting random variable which does not depend on $\\{\\xi_n\\}_{n\\ge1}$). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-05-26T15:05:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "randomly stopped sums",
      "distribution tails",
      "lower limits",
      "equivalences",
      "compound poisson distributions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1920D"
    }
  }
}