{
  "id": "1306.1998",
  "version": "v1",
  "published": "2013-06-09T09:20:59.000Z",
  "updated": "2013-06-09T09:20:59.000Z",
  "title": "Large Deviations of Shepp Statistics for Fractional Brownian Motion",
  "authors": [
    "Enkelejd Hashorva",
    "Zhongquan Tan"
  ],
  "comment": "8 pages",
  "doi": "10.1016/j.spl.2013.06.013",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Define the incremental fractional Brownian field $B_{H}(s+\\tau)-B_{H}(s), H\\in (0,1)$, where $B_{H}(s)$ is a standard fractional Brownian motion with Hurst index $H\\in(0,1)$. In this paper we derive the exact asymptotic behaviour of the maximum $\\max_{(\\tau,s)\\in[0,1]\\times[0,T]} (B_{H}(s+\\tau)-B_{H}(s)) $ for any $H\\in (0,1/2)$ complimenting thus the result of Zholud (2008) for the Brownian motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-09T09:20:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G70"
    ],
    "keywords": [
      "shepp statistics",
      "large deviations",
      "incremental fractional brownian field",
      "standard fractional brownian motion",
      "exact asymptotic behaviour"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.1998H"
    }
  }
}