{
  "id": "1002.4297",
  "version": "v2",
  "published": "2010-02-23T11:08:06.000Z",
  "updated": "2010-09-04T04:15:40.000Z",
  "title": "Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients",
  "authors": [
    "Xicheng Zhang"
  ],
  "comment": "23Pages. Some details were added",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "In this article we prove the existence and uniqueness for degenerate stochastic differential equations with Sobolev (possibly singular) drift and diffusion coefficients in a generalized sense. In particular, our result covers the classical DiPerna-Lions flows and, we also obtain the well-posedness for degenerate Fokker-Planck equations with irregular coefficients. Moreover, a large deviation principle of Freidlin-Wenzell type for this type of SDEs is established.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-04T04:15:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10"
    ],
    "keywords": [
      "sobolev coefficients",
      "degenerate sdes",
      "well-posedness",
      "degenerate stochastic differential equations",
      "large deviation principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.4297Z"
    }
  }
}