{
  "id": "0911.0077",
  "version": "v3",
  "published": "2009-11-02T13:45:06.000Z",
  "updated": "2009-11-09T12:00:42.000Z",
  "title": "Notes on the Cauchy Problem for Backward Stochastic Partial Differential Equations",
  "authors": [
    "Kai Du",
    "Qingxin Meng"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in the whole Euclidean space. Improved existence and uniqueness results are given in the Sobolev space $H^n$ ($=W^n_2$) under weaker assumptions than those used by X. Zhou [Journal of Functional Analysis 103, 275--293 (1992)]. As an application, a comparison theorem is obtained.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-11-09T12:00:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60"
    ],
    "keywords": [
      "backward stochastic partial differential equations",
      "cauchy problem",
      "parabolic type",
      "euclidean space",
      "uniqueness results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.0077D"
    }
  }
}