{
  "id": "1111.6331",
  "version": "v3",
  "published": "2011-11-28T02:26:10.000Z",
  "updated": "2013-07-03T18:54:40.000Z",
  "title": "A wavelet-based approximation of fractional Brownian motion with a parallel algorithm",
  "authors": [
    "Dawei Hong",
    "Shushuang Man",
    "Jean-Camille Birget",
    "Desmond Lun"
  ],
  "comment": "20 pages. J. of Applied Probability, to appear in March 2014",
  "categories": [
    "math.PR"
  ],
  "abstract": "We construct a wavelet-based almost sure uniform approximation of fractional Brownian motion (fBm) B_t^(H), t in [0, 1], of Hurst index H in (0, 1). Our results show that by Haar wavelets which merely have one vanishing moment, an almost sure uniform expansion of fBm of H in (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an fBm efficiently.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-03T18:54:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional brownian motion",
      "parallel algorithm",
      "wavelet-based approximation",
      "sure uniform approximation",
      "generates sample paths"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.6331H"
    }
  }
}