{
  "id": "math/0407377",
  "version": "v2",
  "published": "2004-07-22T10:47:51.000Z",
  "updated": "2005-03-09T14:23:48.000Z",
  "title": "Lévy processes and Jacobi fields",
  "authors": [
    "Eugene Lytvynov"
  ],
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We review the recent results on the Jacobi field of a (real-valued) L\\'evy process defined on a Riemannian manifold. In the case where the L\\'evy process is neither Gaussian, nor Poisson, the corresponding Jacobi field acts in an extended Fock space. We also give a unitary equivalent representation of the Jacobi field in a usual Fock space. This representation is inspired by a result by Accardi, Franz, and Skeide (2002).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-03-09T14:23:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60G57",
      "60H40"
    ],
    "keywords": [
      "lévy processes",
      "levy process",
      "usual fock space",
      "unitary equivalent representation",
      "corresponding jacobi field acts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7377L"
    }
  }
}