{
  "id": "0804.2528",
  "version": "v1",
  "published": "2008-04-16T06:11:26.000Z",
  "updated": "2008-04-16T06:11:26.000Z",
  "title": "Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion",
  "authors": [
    "Jean-Christophe Breton",
    "Ivan Nourdin"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $q\\geq 2$ be a positive integer, $B$ be a fractional Brownian motion with Hurst index $H\\in(0,1)$, $Z$ be an Hermite random variable of index $q$, and $H_q$ denote the Hermite polynomial having degree $q$. For any $n\\geq 1$, set $V_n=\\sum_{k=0}^{n-1} H_q(B_{k+1}-B_k)$. The aim of the current paper is to derive, in the case when the Hurst index verifies $H>1-1/(2q)$, an upper bound for the total variation distance between the laws $\\mathscr{L}(Z_n)$ and $\\mathscr{L}(Z)$, where $Z_n$ stands for the correct renormalization of $V_n$ which converges in distribution towards $Z$. Our results should be compared with those obtained recently by Nourdin and Peccati (2007) in the case when $H<1-1/(2q)$, corresponding to the situation where one has normal approximation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-16T06:11:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G15",
      "60H07"
    ],
    "keywords": [
      "fractional brownian motion",
      "hermite power variations",
      "error bounds",
      "non-normal approximation",
      "total variation distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.2528B"
    }
  }
}