{
  "id": "math/0412200",
  "version": "v1",
  "published": "2004-12-09T21:06:01.000Z",
  "updated": "2004-12-09T21:06:01.000Z",
  "title": "Large deviations for rough paths of the fractional Brownian motion",
  "authors": [
    "Annie Millet",
    "Marta Sanz-Solé"
  ],
  "comment": "32 pages",
  "doi": "10.1016/j.anihpb.2005.04.003",
  "categories": [
    "math.PR"
  ],
  "abstract": "Starting from the construction of a geometric rough path associated with a fractional Brownian motion with Hurst parameter $H\\in]{1/4}, {1/2}[$ given by Coutin and Qian (2002), we prove a large deviation principle in the space of geometric rough paths, extending classical results on Gaussian processes. As a by-product, geometric rough paths associated to elements of the reproducing kernel Hilbert space of the fractional Brownian motion are obtained and an explicit integral representation is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-09T21:06:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60F10"
    ],
    "keywords": [
      "fractional brownian motion",
      "explicit integral representation",
      "large deviation principle",
      "reproducing kernel hilbert space",
      "geometric rough paths"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12200M"
    }
  }
}