{
  "id": "0901.4925",
  "version": "v1",
  "published": "2009-01-30T16:35:18.000Z",
  "updated": "2009-01-30T16:35:18.000Z",
  "title": "Parameter estimation for fractional Ornstein-Uhlenbeck processes",
  "authors": [
    "Yaozhong Hu",
    "David Nualart"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We study a least squares estimator $\\hat {\\theta}_T$ for the Ornstein-Uhlenbeck process, $dX_t=\\theta X_t dt+\\sigma dB^H_t$, driven by fractional Brownian motion $B^H$ with Hurst parameter $H\\ge \\frac12$. We prove the strong consistence of $\\hat {\\theta}_T$ (the almost surely convergence of $\\hat {\\theta}_T$ to the true parameter ${% \\theta}$). We also obtain the rate of this convergence when $1/2\\le H<3/4$, applying a central limit theorem for multiple Wiener integrals. This least squares estimator can be used to study other more simulation friendly estimators such as the estimator $\\tilde \\theta_T$ defined by (4.1).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-30T16:35:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60Hxx"
    ],
    "keywords": [
      "fractional ornstein-uhlenbeck processes",
      "parameter estimation",
      "squares estimator",
      "multiple wiener integrals",
      "central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}