{
  "id": "1003.2122",
  "version": "v1",
  "published": "2010-03-10T14:51:43.000Z",
  "updated": "2010-03-10T14:51:43.000Z",
  "title": "Right inverses of Levy processes: the excursion measure in the general case",
  "authors": [
    "Mladen Savov",
    "Matthias Winkel"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This article is about right inverses of Levy processes as first introduced by Evans in the symmetric case and later studied systematically by the present authors and their co-authors. Here we add to the existing fluctuation theory an explicit description of the excursion measure away from the (minimal) right inverse. This description unifies known formulas in the case of a positive Gaussian coefficient and in the bounded variation case. While these known formulas relate to excursions away from a point starting negative continuously, and excursions started by a jump, the present description is in terms of excursions away from the supremum continued up to a return time. In the unbounded variation case with zero Gaussian coefficient previously excluded, excursions start negative continuously, but the excursion measures away from the right inverse and away from a point are mutually singular. We also provide a new construction and a new formula for the Laplace exponent of the minimal right inverse.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-10T14:51:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51"
    ],
    "keywords": [
      "levy processes",
      "general case",
      "variation case",
      "excursions start",
      "excursions away"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.2122S"
    }
  }
}