{
  "id": "0803.3716",
  "version": "v1",
  "published": "2008-03-26T12:47:19.000Z",
  "updated": "2008-03-26T12:47:19.000Z",
  "title": "On distributional properties of perpetuities",
  "authors": [
    "Gerold Alsmeyer",
    "Alex Iksanov",
    "Uwe Roesler"
  ],
  "comment": "to appear in Journal of Theoretical Probability",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously singular. We further provide necessary and sufficient criteria for the finiteness of $p$-moments, $p>0$ as well as exponential moments. In particular, a formula for the abscissa of convergence of the moment generating function is provided. The results are illustrated with a number of examples at the end of the article.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-26T12:47:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E99",
      "60G50"
    ],
    "keywords": [
      "distributional properties",
      "perpetuities",
      "study probability distributions",
      "convergent random series",
      "special structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.3716A"
    }
  }
}