{
  "id": "1804.07069",
  "version": "v1",
  "published": "2018-04-19T10:21:38.000Z",
  "updated": "2018-04-19T10:21:38.000Z",
  "title": "On distributions of exponential functionals of the processes with independent increments",
  "authors": [
    "L. Vostrikova"
  ],
  "comment": "22 pages, no comments",
  "categories": [
    "math.PR"
  ],
  "abstract": "The aim of this paper is to study the laws of the exponential functionals of the processes $X$ with independent increments, namely $$I_t= \\int _0^t\\exp(-X_s)ds, \\,\\, t\\geq 0,$$ and also $$I_{\\infty}= \\int _0^{\\infty}\\exp(-X_s)ds.$$ Under suitable conditions we derive the integro-differential equations for the density of $I_t$ and $I_{\\infty}$. We give sufficient conditions for the existence of smooth density of the laws of these functionals. In the particular case of Levy processes these equations can be simplified and, in a number of cases, solved explicitly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-19T10:21:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "91G80"
    ],
    "keywords": [
      "exponential functionals",
      "independent increments",
      "distributions",
      "levy processes",
      "smooth density"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}