{
  "id": "0805.3394",
  "version": "v1",
  "published": "2008-05-22T07:16:37.000Z",
  "updated": "2008-05-22T07:16:37.000Z",
  "title": "Estimation in models driven by fractional Brownian motion",
  "authors": [
    "Corinne Berzin",
    "José R. León"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/07-AIHP105 the Annales de l'Institut Henri Poincar\\'e - Probabilit\\'es et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annales de l'Institut Henri Poincar\\'e - Probabilit\\'es et Statistiques 2008, Vol. 44, No. 2, 191-213",
  "doi": "10.1214/07-AIHP105",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\{b_H(t),t\\in\\mathbb{R}\\}$ be the fractional Brownian motion with parameter $0<H<1$. When $1/2<H$, we consider diffusion equations of the type \\[X(t)=c+\\int_0^t\\sigma\\bigl(X(u)\\bigr)\\mathrm {d}b_H(u)+\\int _0^t\\mu\\bigl(X(u)\\bigr)\\mathrm {d}u.\\] In different particular models where $\\sigma(x)=\\sigma$ or $\\sigma(x)=\\sigma x$ and $\\mu(x)=\\mu$ or $\\mu(x)=\\mu x$, we propose a central limit theorem for estimators of $H$ and of $\\sigma$ based on regression methods. Then we give tests of the hypothesis on $\\sigma$ for these models. We also consider functional estimation on $\\sigma(\\cdot)$ in the above more general models based in the asymptotic behavior of functionals of the 2nd-order increments of the fBm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-22T07:16:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G15",
      "60G18",
      "60H10",
      "62F03",
      "62F12",
      "33C45"
    ],
    "keywords": [
      "fractional brownian motion",
      "models driven",
      "central limit theorem",
      "asymptotic behavior",
      "diffusion equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008AnIHP..44..191B"
    }
  }
}