{
  "id": "1207.6165",
  "version": "v2",
  "published": "2012-07-26T04:24:48.000Z",
  "updated": "2013-07-09T05:07:49.000Z",
  "title": "Anticipated backward doubly stochastic differential equations",
  "authors": [
    "Xiaoming Xu"
  ],
  "comment": "17 pages",
  "journal": "Applied Mathematics and Computation, 2013, 220:53-62",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we deal with a new type of differential equations called anticipated backward doubly stochastic differential equations (anticipated BDSDEs). The coefficients of these BDSDEs depend on the future value of the solution $(Y, Z)$. We obtain the existence and uniqueness theorem and a comparison theorem for the solutions of these equations. Besides, as an application, we also establish a duality between the anticipated BDSDEs and the delayed doubly stochastic differential equations (delayed DSDEs).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-09T05:07:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H05",
      "60H10"
    ],
    "keywords": [
      "backward doubly stochastic differential equations",
      "anticipated backward doubly stochastic differential",
      "anticipated bdsdes",
      "delayed doubly stochastic differential equations",
      "bdsdes depend"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.6165X"
    }
  }
}