{
  "id": "1011.5600",
  "version": "v3",
  "published": "2010-11-25T11:43:45.000Z",
  "updated": "2011-01-14T04:17:20.000Z",
  "title": "Discontinuous Stochastic Differential Equations Driven by Lévy Processes",
  "authors": [
    "Xicheng Zhang"
  ],
  "comment": "20pp, improve some statements",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "In this article we prove the pathwise uniqueness for stochastic differential equations in $\\mR^d$ with time-dependent Sobolev drifts, and driven by symmetric $\\alpha$-stable processes provided that $\\alpha\\in(1,2)$ and its spectral measure is non-degenerate. In particular, the drift is allowed to have jump discontinuity when $\\alpha\\in(\\frac{2d}{d+1},2)$. Our proof is based on some estimates of Krylov's type for purely discontinuous semimartingales.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-01-14T04:17:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10"
    ],
    "keywords": [
      "discontinuous stochastic differential equations driven",
      "lévy processes",
      "time-dependent sobolev drifts",
      "jump discontinuity",
      "spectral measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.5600Z"
    }
  }
}