{
  "id": "math/0504559",
  "version": "v1",
  "published": "2005-04-27T22:00:03.000Z",
  "updated": "2005-04-27T22:00:03.000Z",
  "title": "Stochastic Differential Equations: A Wiener Chaos Approach",
  "authors": [
    "S. V. Lototsky",
    "B. L. Rozovskii"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of ordinary and partial differential equations driven by finite- or infinite-dimensional noise with either adapted or anticipating input. Existence, uniqueness, regularity, and probabilistic representation of this Wiener Chaos solution is established for a large class of equations. A number of examples are presented to illustrate the general constructions. A detailed analysis is presented for the various forms of the passive scalar equation and for the first-order It\\^{o} stochastic partial differential equation. Applications to nonlinear filtering if diffusion processes and to the stochastic Navier-Stokes equation are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-27T22:00:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15"
    ],
    "keywords": [
      "stochastic differential equations",
      "wiener chaos approach",
      "stochastic partial differential equation",
      "partial differential equations driven",
      "stochastic navier-stokes equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4559L"
    }
  }
}