{
  "id": "0911.1897",
  "version": "v1",
  "published": "2009-11-10T12:31:08.000Z",
  "updated": "2009-11-10T12:31:08.000Z",
  "title": "The longest excursion of fractional Brownian motion : numerical evidence of non-Markovian effects",
  "authors": [
    "Reinaldo Garcia-Garcia",
    "Alberto Rosso",
    "Gregory Schehr"
  ],
  "comment": "4 pages, 4 figures",
  "journal": "Phys. Rev. E 81, 010102(R) (2010)",
  "doi": "10.1103/PhysRevE.81.010102",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "We study, using exact numerical simulations, the statistics of the longest excursion l_{\\max}(t) up to time t for the fractional Brownian motion with Hurst exponent 0<H<1. We show that in the large t limit, < l_{\\max}(t) > \\propto Q_\\infty t where Q_\\infty \\equiv Q_\\infty(H) depends continuously on H, and in a non trivial way. These results are compared with exact analytical results obtained recently for a renewal process with an associated persistence exponent \\theta = 1-H. This comparison shows that Q_\\infty(H) carries the clear signature of non-Markovian effects for H\\neq 1/2. The pre-asymptotic behavior of < l_{\\max}(t)> is also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-10T12:31:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.40.-a",
      "02.50.-r",
      "05.70.Ln"
    ],
    "keywords": [
      "fractional brownian motion",
      "longest excursion",
      "non-markovian effects",
      "numerical evidence",
      "non trivial way"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2010,
      "month": "Jan",
      "volume": 81,
      "number": 1,
      "pages": "010102"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010PhRvE..81a0102G"
    }
  }
}