{
  "id": "math/0505551",
  "version": "v3",
  "published": "2005-05-25T21:43:31.000Z",
  "updated": "2008-12-02T18:26:20.000Z",
  "title": "Stochastic Differential Equations Driven by Purely Spatial Noise",
  "authors": [
    "S. V. Lototsky",
    "B. L. Rozovskii"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We study stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron-Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven by space-only noise. The paper presents results about solvability of such equations in weighted Wiener chaos spaces and studies the long-time behavior of the solutions of evolution equations with space-only noise.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-12-02T18:26:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H40",
      "35R60"
    ],
    "keywords": [
      "stochastic differential equations driven",
      "purely spatial noise",
      "study stochastic parabolic",
      "weighted wiener chaos spaces",
      "space-only noise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5551L"
    }
  }
}