{
  "id": "0908.2695",
  "version": "v2",
  "published": "2009-08-19T08:29:44.000Z",
  "updated": "2009-08-24T02:34:46.000Z",
  "title": "Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients",
  "authors": [
    "Xicheng Zhang"
  ],
  "comment": "32",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "In this article, using DiPerna-Lions theory \\cite{Di-Li}, we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the $L^1$-integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinear filtering problem and also obtain the existence and uniqueness of generalized solutions for a degenerate nonlinear SPDE.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-24T02:34:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35K15"
    ],
    "keywords": [
      "degenerate coefficients",
      "second order stochastic partial differential",
      "order stochastic partial differential equations",
      "linear second order stochastic partial",
      "degenerate nonlinear spde"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2695Z"
    }
  }
}