{
  "id": "0907.4866",
  "version": "v3",
  "published": "2009-07-28T08:49:21.000Z",
  "updated": "2009-08-18T08:12:02.000Z",
  "title": "Stochastic Flows of SDEs with Irregular Coefficients and Stochastic Transport Equations",
  "authors": [
    "Xicheng Zhang"
  ],
  "comment": "32Pages, add the existence of invariant measures",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere stochastic (invertible) flow associated with the SDE in the sense of Lebesgue measure. In the case of constant diffusions and BV drifts, we obtain such a result by studying the related stochastic transport equation. In the case of non-constant diffusions and Sobolev drifts, we use a direct method. In particular, we extend the recent results on ODEs with non-smooth vector fields to SDEs. Moreover, we also give a criterion for the existence of invariant measures for the associated transition semigroup.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-08-18T08:12:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H15"
    ],
    "keywords": [
      "irregular coefficients",
      "stochastic flows",
      "non-smooth vector fields",
      "stochastic differential equations",
      "related stochastic transport equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.4866Z"
    }
  }
}