{
  "id": "1208.1665",
  "version": "v1",
  "published": "2012-08-08T13:50:35.000Z",
  "updated": "2012-08-08T13:50:35.000Z",
  "title": "Solutions of martingale problems for Lévy-type operators and stochastic differential equations driven by Lévy processes with discontinuous coefficients",
  "authors": [
    "Peter Imkeller",
    "Niklas Willrich"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We show the existence of L\\'evy-type stochastic processes in one space dimension with characteristic triplets that are either discontinuous at thresholds, or are stable-like with stability index functions for which the closures of the discontinuity sets are countable. For this purpose, we formulate the problem in terms of a Skorokhod-space martingale problem associated with non-local operators with discontinuous coefficients. These operators are approximated along a sequence of smooth non-local operators giving rise to Feller processes with uniformly controlled symbols. They converge uniformly outside of increasingly smaller neighborhoods of a Lebesgue nullset on which the singularities of the limit operator are located.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-08T13:50:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60H10",
      "60J75",
      "60G46",
      "60G52",
      "47G30"
    ],
    "keywords": [
      "stochastic differential equations driven",
      "martingale problem",
      "discontinuous coefficients",
      "lévy processes",
      "lévy-type operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1665I"
    }
  }
}