{
  "id": "0801.2959",
  "version": "v1",
  "published": "2008-01-18T19:34:06.000Z",
  "updated": "2008-01-18T19:34:06.000Z",
  "title": "On Besov regularity of Brownian motions in infinite dimensions",
  "authors": [
    "Tuomas Hytonen",
    "Mark Veraar"
  ],
  "comment": "to appear in Probab. Math. Statist (2008)",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We extend to the vector-valued situation some earlier work of Ciesielski and Roynette on the Besov regularity of the paths of the classical Brownian motion. We also consider a Brownian motion as a Besov space valued random variable. It turns out that a Brownian motion, in this interpretation, is a Gaussian random variable with some pathological properties. We prove estimates for the first moment of the Besov norm of a Brownian motion. To obtain such results we estimate expressions of the form $\\E \\sup_{n\\geq 1}\\|\\xi_n\\|$, where the $\\xi_n$ are independent centered Gaussian random variables with values in a Banach space. Using isoperimetric inequalities we obtain two-sided inequalities in terms of the first moments and the weak variances of $\\xi_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-18T19:34:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "28C20",
      "46E40",
      "60G17"
    ],
    "keywords": [
      "brownian motion",
      "besov regularity",
      "infinite dimensions",
      "space valued random variable",
      "first moment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}