{
  "id": "0912.0131",
  "version": "v1",
  "published": "2009-12-01T12:04:23.000Z",
  "updated": "2009-12-01T12:04:23.000Z",
  "title": "Some applications of duality for Lévy processes in a half-line",
  "authors": [
    "Jean Bertoin",
    "Mladen Savov"
  ],
  "doi": "10.1112/blms/bdq084",
  "categories": [
    "math.PR"
  ],
  "abstract": "The central result of this paper is an analytic duality relation for real-valued L\\'evy processes killed upon exiting a half-line. By Nagasawa's theorem, this yields a remarkable time-reversal identity involving the L\\'evy process conditioned to stay positive. As examples of applications, we construct a version of the L\\'evy process indexed by the entire real line and started from $-\\infty$ which enjoys a natural spatial-stationarity property, and point out that the latter leads to a natural Lamperti-type representation for self-similar Markov processes in $(0,\\infty)$ started from the entrance point 0+.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-01T12:04:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60J45",
      "60G18"
    ],
    "keywords": [
      "lévy processes",
      "applications",
      "self-similar markov processes",
      "natural lamperti-type representation",
      "natural spatial-stationarity property"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.0131B"
    }
  }
}