{
  "id": "1310.4955",
  "version": "v2",
  "published": "2013-10-18T09:06:26.000Z",
  "updated": "2014-11-18T12:41:48.000Z",
  "title": "On exponential functionals, harmonic potential measures and undershoots of subordinators",
  "authors": [
    "Larbi Alili",
    "Wissem Jedidi",
    "Víctor Rivero"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish a link between the distribution of an exponential functional I and the undershoots of a subordinator, which is given in terms of the associated harmonic potential measure. This allows us to give a necessary and sufficient condition in terms of the L\\'evy measure for the exponential functional to be multiplicative infinitely divisible. We then provide a formula for the moment generating function of an exponential functional $I$ and the so called remainder random variable $R$ associated to it. We provide a realization of the remainder random variable $R$ as an infinite product involving independent last position random variables of the subordinator. Some properties of harmonic measures are obtained and some examples are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-18T09:06:26.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-18T12:41:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60E10",
      "60E07"
    ],
    "keywords": [
      "exponential functional",
      "subordinator",
      "undershoots",
      "remainder random variable",
      "position random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4955A"
    }
  }
}