{
  "id": "0802.3307",
  "version": "v2",
  "published": "2008-02-22T12:47:17.000Z",
  "updated": "2009-12-14T14:03:19.000Z",
  "title": "Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case $H=1/4$",
  "authors": [
    "Ivan Nourdin",
    "Anthony Réveillac"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AOP473 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2009, Vol. 37, No. 6, 2200-2230",
  "doi": "10.1214/09-AOP473",
  "categories": [
    "math.PR"
  ],
  "abstract": "We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion $B$ with Hurst index $H=1/4$. This completes the only missing case in a very recent work by I. Nourdin, D. Nualart and C. A. Tudor. Moreover, as an application, we solve a recent conjecture of K. Burdzy and J. Swanson on the asymptotic behavior of the Riemann sums with alternating signs associated to $B$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-12-14T14:03:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60H05",
      "60G15",
      "60H07"
    ],
    "keywords": [
      "fractional brownian motion",
      "weighted quadratic variations",
      "asymptotic behavior",
      "critical case",
      "hurst index"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.3307N"
    }
  }
}