{
  "id": "0712.2219",
  "version": "v4",
  "published": "2007-12-13T19:05:29.000Z",
  "updated": "2008-11-12T20:12:08.000Z",
  "title": "Representation theorems for backward doubly stochastic differential equations",
  "authors": [
    "Auguste Aman"
  ],
  "comment": "The version of this article have 20 pages and is submitted to Journal Bernoulli for publication",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study the class of backward doubly stochastic differential equations (BDSDEs, for short) whose terminal value depends on the history of forward diffusion. We first establish a probabilistic representation for the spatial gradient of the stochastic viscosity solution to a quasilinear parabolic SPDE in the spirit of the Feynman-Kac formula, without using the derivatives of the coefficients of the corresponding BDSDE. Then such a representation leads to a closed-form representation of the martingale integrand of BDSDE, under only standard Lipschitz condition on the coefficients.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2008-11-12T20:12:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H20"
    ],
    "keywords": [
      "backward doubly stochastic differential equations",
      "representation theorems",
      "standard lipschitz condition",
      "terminal value depends",
      "quasilinear parabolic spde"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.2219A"
    }
  }
}