{
  "id": "1802.03496",
  "version": "v1",
  "published": "2018-02-10T01:50:55.000Z",
  "updated": "2018-02-10T01:50:55.000Z",
  "title": "On the maximum of discretely sampled fractional Brownian motion with small Hurst parameter",
  "authors": [
    "Konstantin Borovkov",
    "Mikhail Zhitlukhin"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that the distribution of the maximum of the fractional Brownian motion $B^H$ with Hurst parameter $H\\to 0$ over an $n$-point set $\\tau \\subset [0,1]$ can be approximated by the normal law with mean $\\sqrt{\\ln n}$ and variance $1/2$ provided that $n\\to \\infty$ slowly enough and the points in $\\tau$ are not too close to each other.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-10T01:50:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60G15",
      "60E15",
      "60F05"
    ],
    "keywords": [
      "discretely sampled fractional brownian motion",
      "small hurst parameter",
      "point set",
      "normal law",
      "distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}