{
  "id": "1212.3832",
  "version": "v3",
  "published": "2012-12-16T21:21:17.000Z",
  "updated": "2014-05-28T15:17:52.000Z",
  "title": "Ornstein-Uhlenbeck processes driven by cylindrical Lévy processes",
  "authors": [
    "Markus Riedle"
  ],
  "comment": "This version is significantly revised and corrected",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article we introduce a theory of integration for deterministic, operator-valued integrands with respect to cylindrical L\\'evy processes in separable Banach spaces. Here, a cylindrical L\\'evy process is understood in the classical framework of cylindrical random variables and cylindrical measures, and thus, it can be considered as a natural generalisation of cylindrical Wiener processes or white noises. Depending on the underlying Banach space, we provide necessary and/or sufficient conditions for a function to be integrable. In the last part, the developed theory is applied to define Ornstein-Uhlenbeck processes driven by cylindrical L\\'evy processes and several examples are considered.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-28T15:17:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H05",
      "47D06",
      "60G20"
    ],
    "keywords": [
      "cylindrical lévy processes",
      "cylindrical levy processes",
      "define ornstein-uhlenbeck processes driven",
      "cylindrical random variables",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.3832R"
    }
  }
}