{
  "id": "1105.1428",
  "version": "v1",
  "published": "2011-05-07T09:00:37.000Z",
  "updated": "2011-05-07T09:00:37.000Z",
  "title": "$W^{m,p}$-Solution ($p\\geq2$) of Linear Degenerate Backward Stochastic Partial Differential Equations in the Whole Space",
  "authors": [
    "Kai Du",
    "Shanjian Tang",
    "Qi Zhang"
  ],
  "comment": "29 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "In this paper, we consider the backward Cauchy problem of linear degenerate stochastic partial differential equations. We obtain the existence and uniqueness results in Sobolev space $L^p(\\Omega; C([0,T];W^{m,p}))$ with both $m\\geq 1$ and $p\\geq 2$ being arbitrary, without imposing the symmetry condition for the coefficient $\\sigma$ of the gradient of the second unknown---which was introduced by Ma and Yong [Prob. Theor. Relat. Fields 113 (1999)] in the case of $p=2$. To illustrate the application, we give a maximum principle for optimal control of degenerate stochastic partial differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-07T09:00:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "93E20"
    ],
    "keywords": [
      "linear degenerate backward stochastic partial",
      "backward stochastic partial differential equations",
      "degenerate backward stochastic partial differential",
      "degenerate stochastic partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.1428D"
    }
  }
}