{
  "id": "1207.2634",
  "version": "v1",
  "published": "2012-07-11T13:33:19.000Z",
  "updated": "2012-07-11T13:33:19.000Z",
  "title": "Stochastic integration with respect to cylindrical Levy processes in Hilbert spaces: an L^2 approach",
  "authors": [
    "Markus Riedle"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this work stochastic integration with respect to cylindrical Levy processes with weak second moments is introduced. It is well known that a deterministic Hilbert-Schmidt operator radonifies a cylindrical random variable, i.e. it maps a cylindrical random variable to a classical Hilbert space valued random variable. Our approach is based on a generalisation of this result to the radonification of the cylindrical increments of a cylindrical Levy process by random Hilbert-Schmidt operators. This generalisation enables us to introduce a Hilbert space valued random variable as the stochastic integral of a predictable stochastic process with respect to a cylindrical Levy process. We finish this work by deriving an Ito isometry and by considering shortly stochastic partial differential equations driven by cylindrical Levy processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-11T13:33:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B11",
      "60G51",
      "60H05",
      "60H15"
    ],
    "keywords": [
      "cylindrical levy processes",
      "space valued random variable",
      "hilbert space valued random",
      "stochastic integration",
      "partial differential equations driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2634R"
    }
  }
}