{
  "id": "1006.5288",
  "version": "v2",
  "published": "2010-06-28T08:44:59.000Z",
  "updated": "2011-05-15T18:08:50.000Z",
  "title": "On the Coupling Property of Lévy Processes",
  "authors": [
    "René L. Schilling",
    "Jian Wang"
  ],
  "comment": "14 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give necessary and sufficient conditions guaranteeing that the coupling for L\\'evy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier results by Mineka and Lindvall-Rogers on couplings of random walks. In particular, we obtain that a L\\'{e}vy process admits a successful coupling, if it is a strong Feller process or if the L\\'evy (jump) measure has an absolutely continuous component.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-05-15T18:08:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60G50",
      "60J25",
      "60J75"
    ],
    "keywords": [
      "lévy processes",
      "coupling property",
      "strong feller process",
      "non-degenerate jump part",
      "compound poisson process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011AnIHP..47.1147S"
    }
  }
}