{
  "id": "0705.0570",
  "version": "v4",
  "published": "2007-05-04T07:28:47.000Z",
  "updated": "2009-01-19T15:54:05.000Z",
  "title": "Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion",
  "authors": [
    "Ivan Nourdin"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/07-AOP385 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2008, Vol. 36, No. 6, 2159-2175",
  "doi": "10.1214/07-AOP385",
  "categories": [
    "math.PR"
  ],
  "abstract": "The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion $B$ with Hurst index $H$. In the quadratic (resp. cubic) case, when $H<1/4$ (resp. $H<1/6$), we show by means of Malliavin calculus that the convergence holds in $L^2$ toward an explicit limit which only depends on $B$. This result is somewhat surprising when compared with the celebrated Breuer and Major theorem.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-01-19T15:54:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G15",
      "60H07"
    ],
    "keywords": [
      "fractional brownian motion",
      "cubic variations",
      "weighted quadratic",
      "asymptotic behavior",
      "fine study"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0570N"
    }
  }
}