{
  "id": "1606.07106",
  "version": "v1",
  "published": "2016-06-11T10:58:03.000Z",
  "updated": "2016-06-11T10:58:03.000Z",
  "title": "A Sufficient Condition for Absolute Continuity of Infinitely Divisible Distributions",
  "authors": [
    "Kasra Alishahi",
    "Erfan Salavati"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider infinitely divisible distributions with symmetric L\\'evy measure and study the absolute continuity of them with respect to the Lebesgue measure. We prove that if $\\eta(r)=\\int_{|x|\\le r} x^2 \\nu(dx)$ where $\\nu$ is the L\\'evy measure, then $\\int_0^1 \\frac{r}{\\eta(r)}dr <\\infty$ is a sufficient condition for absolute continuity. As far as we know, our result is not implied by existing results about absolute continuity of infinitely divisible distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-11T10:58:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E07",
      "60G51"
    ],
    "keywords": [
      "infinitely divisible distributions",
      "absolute continuity",
      "sufficient condition",
      "symmetric levy measure",
      "lebesgue measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}