{
  "id": "0912.1694",
  "version": "v3",
  "published": "2009-12-09T13:20:19.000Z",
  "updated": "2010-02-08T17:22:00.000Z",
  "title": "Perpetuities with thin tails revisited",
  "authors": [
    "Paweł Hitczenko",
    "Jacek Wesołowski"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AAP603 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org). This version corrects formula (6.1) in the statement of Theorem 6 in published version",
  "journal": "Annals of Applied Probability 2009, Vol. 19, No. 6, 2080-2101",
  "doi": "10.1214/09-AAP603",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the tail behavior of random variables $R$ which are solutions of the distributional equation $R\\stackrel{d}{=}Q+MR$, where $(Q,M)$ is independent of $R$ and $|M|\\le 1$. Goldie and Gr\\\"{u}bel showed that the tails of $R$ are no heavier than exponential and that if $Q$ is bounded and $M$ resembles near 1 the uniform distribution, then the tails of $R$ are Poissonian. In this paper, we further investigate the connection between the tails of $R$ and the behavior of $M$ near 1. We focus on the special case when $Q$ is constant and $M$ is nonnegative.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-02-08T17:22:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H25",
      "60E99"
    ],
    "keywords": [
      "thin tails",
      "perpetuities",
      "random variables",
      "distributional equation",
      "special case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1694H"
    }
  }
}