{
  "id": "1702.00778",
  "version": "v1",
  "published": "2017-02-02T18:30:24.000Z",
  "updated": "2017-02-02T18:30:24.000Z",
  "title": "Transition probabilities of Lévy-type processes: Parametrix construction",
  "authors": [
    "Franziska Kühn"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We present an existence result for L\\'evy-type processes which requires only weak regularity assumptions on the symbol $q(x,\\xi)$ with respect to the space variable $x$. Applications range from existence and uniqueness results for L\\'evy-driven SDEs with H\\\"{o}lder continuous coefficients to existence results for stable-like processes and L\\'evy-type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of L\\'evy and L\\'evy-type processes. The paper includes an extensive list of L\\'evy(-type) processes satisfying the assumptions of our results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-02T18:30:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J35",
      "60J25",
      "60G51",
      "60H10",
      "60J75",
      "35S05"
    ],
    "keywords": [
      "lévy-type processes",
      "parametrix construction",
      "transition probabilities",
      "levy-type processes",
      "existence result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}