{
  "id": "1011.1067",
  "version": "v3",
  "published": "2010-11-04T07:07:46.000Z",
  "updated": "2012-12-05T12:39:52.000Z",
  "title": "Coupling property and gradient estimates of Lévy processes via the symbol",
  "authors": [
    "René L. Schilling",
    "Paweł Sztonyk",
    "Jian Wang"
  ],
  "comment": "Published in at http://dx.doi.org/10.3150/11-BEJ375 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)",
  "journal": "Bernoulli 2012, Vol. 18, No. 4, 1128-1149",
  "doi": "10.3150/11-BEJ375",
  "categories": [
    "math.PR",
    "math.FA",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We derive explicitly the coupling property for the transition semigroup of a L\\'{e}vy process and gradient estimates for the associated semigroup of transition operators. This is based on the asymptotic behaviour of the symbol or the characteristic exponent near zero and infinity, respectively. Our results can be applied to a large class of L\\'{e}vy processes, including stable L\\'{e}vy processes, layered stable processes, tempered stable processes and relativistic stable processes.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-05T12:39:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gradient estimates",
      "coupling property",
      "lévy processes",
      "transition semigroup",
      "relativistic stable processes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.1067S"
    }
  }
}