{
  "id": "0808.3458",
  "version": "v2",
  "published": "2008-08-26T09:00:10.000Z",
  "updated": "2008-08-29T13:24:51.000Z",
  "title": "A central limit theorem for the rescaled Lévy area of two-dimensional fractional Brownian motion with Hurst index $H<1/4$",
  "authors": [
    "Jeremie Unterberger"
  ],
  "comment": "70 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $B=(B^{(1)},B^{(2)})$ be a two-dimensional fractional Brownian motion with Hurst index $\\alpha\\in (0,1/4)$. Using an analytic approximation $B(\\eta)$ of $B$ introduced in \\cite{Unt08}, we prove that the rescaled L\\'evy area process $(s,t)\\to \\eta^{\\half(1-4\\alpha)}\\int_s^t dB_{t_1}^{(1)}(\\eta) \\int_s^{t_1} dB_{t_2}^{(2)}(\\eta)$ converges in law to $W_t-W_s$ where $W$ is a Brownian motion independent from $B$. The method relies on a very general scheme of analysis of singularities of analytic functions, applied to the moments of finite-dimensional distributions of the L\\'evy area.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-29T13:24:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G15",
      "60G18",
      "60H05"
    ],
    "keywords": [
      "two-dimensional fractional brownian motion",
      "central limit theorem",
      "rescaled lévy area",
      "hurst index",
      "levy area"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 70,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.3458U"
    }
  }
}