{
  "id": "1010.5941",
  "version": "v3",
  "published": "2010-10-28T12:36:59.000Z",
  "updated": "2013-03-31T13:17:09.000Z",
  "title": "Uniqueness in Law of the stochastic convolution process driven by Lévy noise",
  "authors": [
    "Zdzisław Brzeźniak",
    "Erika Hausenblas",
    "Elżbieta Motyl"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We will give a proof of the following fact. If $\\mathfrak{A}_1$ and $\\mathfrak{A}_2$, $\\tilde \\eta_1$ and $\\tilde \\eta_2$, $\\xi_1$ and $\\xi_2$ are two examples of filtered probability spaces, time homogeneous compensated Poisson random measures, and progressively measurable Banach space valued processes such that the laws on $L^p([0,T],{L}^{p}(Z,\\nu ;E))\\times \\CM_I([0,T]\\times Z)$ of the pairs $(\\xi_1,\\eta_1)$ and $(\\xi_2,\\eta_2)$ %, $i=1,2$, are equal, and $u_1$ and $u_2$ are the corresponding stochastic convolution processes, then the laws on $ (\\DD([0,T];X)\\cap L^p([0,T];B)) \\times L^p([0,T],{L}^{p}(Z,\\nu ;E))\\times \\CM_I([0,T]\\times Z) $, where $B \\subset E \\subset X$, of the triples $(u_i,\\xi_i,\\eta_i)$, $i=1,2$, are equal as well. By $\\DD([0,T];X)$ we denote the Skorokhod space of $X$-valued processes.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-03-31T13:17:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G57"
    ],
    "keywords": [
      "stochastic convolution process driven",
      "lévy noise",
      "banach space valued processes",
      "compensated poisson random measures",
      "homogeneous compensated poisson random"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.5941B"
    }
  }
}