{
  "id": "2008.06308",
  "version": "v1",
  "published": "2020-08-14T11:56:43.000Z",
  "updated": "2020-08-14T11:56:43.000Z",
  "title": "Time regularity of Lévy-type evolution in Hilbert spaces and of some $α$-stable processes",
  "authors": [
    "Witold Bednorz",
    "Anna Talarczyk"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we consider the existence of weakly c\\`adl\\`ag versions of a solution to a linear equation in a Hilbert space $H$, driven by a Levy process taking values in a Hilbert space $U$. In particular we are interested in diagonal type processes, where process on coordinates are functionals of independent $\\alpha$ stable symmetric process. We give the if and only if characterization in this case. We apply the same techniques to obtain a sufficient condition for existence of a c\\`adl\\`ag versions of stable processes described as integrals of deterministic functions with respect to symmetric $\\alpha$-stable random measures with $\\alpha\\in[1,2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-14T11:56:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G52",
      "60G17"
    ],
    "keywords": [
      "hilbert space",
      "stable processes",
      "lévy-type evolution",
      "time regularity",
      "diagonal type processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}