{
  "id": "1003.3978",
  "version": "v2",
  "published": "2010-03-21T07:54:36.000Z",
  "updated": "2011-10-16T12:38:41.000Z",
  "title": "A General Construction to Stationary Weak Solutions of Parabolic SPDEs",
  "authors": [
    "Huinan Leng",
    "Qi Zhang"
  ],
  "comment": "Part of contents will be included in a new paper",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we construct the stationary weak solutions of parabolic SPDEs by a general infinite horizon backward doubly stochastic differential equations (BDSDEs for short) with non-degenerate terminal functions. For this, we first study the existence, uniqueness and stationarity of solutions of such kind of BDSDEs in weighted $L^p(dx)\\bigotimes L^2(dx)$ space ($p>2$). Then the corresponding stationary solutions of parabolic SPDEs can be obtained by the connection between the solutions of BDSDEs in weighted $L^p(dx)\\bigotimes L^2(dx)$ space and the weak solutions of parabolic SPDEs. This result shows that the stationary solutions of SPDEs can be constructed by their corresponding infinite horizon BDSDEs with any Lipschitz continuous terminal function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-16T12:38:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H10",
      "37H10"
    ],
    "keywords": [
      "stationary weak solutions",
      "parabolic spdes",
      "general construction",
      "doubly stochastic differential equations",
      "horizon backward doubly stochastic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.3978L"
    }
  }
}