{
  "id": "math/0702049",
  "version": "v1",
  "published": "2007-02-02T13:12:32.000Z",
  "updated": "2007-02-02T13:12:32.000Z",
  "title": "A large deviation principle in Hölder norm for multiple fractional integrals",
  "authors": [
    "Marta Sanz-Solé",
    "Iván Torrecilla-Tarantino"
  ],
  "comment": "23 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "For a fractional Brownian motion $B^H$ with Hurst parameter $H\\in]{1/4},{1/2}[\\cup]{1/2},1[$, multiple indefinite integrals on a simplex are constructed and the regularity of their sample paths are studied. Then, it is proved that the family of probability laws of the processes obtained by replacing $B^H$ by $\\epsilon^{{1/2}} B^H$ satisfies a large deviation principle in H\\\"older norm. The definition of the multiple integrals relies upon a representation of the fractional Brownian motion in terms of a stochastic integral with respect to a standard Brownian motion. For the large deviation principle, the abstract general setting given by Ledoux in [Lecture Notes in Math., vol. 1426 (1990) 1-14] is used.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-02T13:12:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G17",
      "60G15",
      "60H07",
      "60H05"
    ],
    "keywords": [
      "large deviation principle",
      "multiple fractional integrals",
      "hölder norm",
      "fractional brownian motion",
      "multiple indefinite integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2049S"
    }
  }
}