{
  "id": "1307.3087",
  "version": "v2",
  "published": "2013-07-11T12:29:56.000Z",
  "updated": "2014-12-30T19:08:12.000Z",
  "title": "Parametrix construction for certain Lévy-type processes",
  "authors": [
    "Victoria Knopova",
    "Alexei Kulik"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we show that a non-local operator of certain type extends to the generator of a strong Markov process, admitting the transition probability density. For this transition probability density we construct the intrinsic upper and lower bounds, and prove some smoothness properties. Some examples are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-11T12:29:56.000Z",
      "title": "Parametrix construction for certain Lévy-type processes and applications",
      "abstract": "We consider the Cauchy problem for a certain class of pseudo-differential operators with continuous negative symbol. Using parametrix method we construct a fundamental solution as well as upper and lower estimates for it. We show that such a solution gives rise to a Feller process. As an application of our estimates we present the criterion for the existence of a local time for the process. Some examples are provided.",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Victoria Knopova",
        "Aleksei Kulik"
      ]
    },
    {
      "version": "v2",
      "updated": "2014-12-30T19:08:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J35",
      "60J75",
      "35S05",
      "35S10",
      "47G30"
    ],
    "keywords": [
      "parametrix construction",
      "lévy-type processes",
      "application",
      "parametrix method",
      "local time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.3087K"
    }
  }
}