{
  "id": "1302.6047",
  "version": "v1",
  "published": "2013-02-25T10:57:28.000Z",
  "updated": "2013-02-25T10:57:28.000Z",
  "title": "Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the Second Kind",
  "authors": [
    "Ehsan Azmoodeh",
    "Jose Igor Morlanes"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Fractional Ornstein-Uhlenbeck process of the second kind $(\\text{fOU}_{2})$ is solution of the Langevin equation $\\mathrm{d}X_t = -\\theta X_t\\,\\mathrm{d}t+\\mathrm{d}Y_t^{(1)}, \\ \\theta >0$ with driving noise $ Y_t^{(1)} := \\int^t_0 e^{-s} \\,\\mathrm{d}B_{a_s}; \\ a_t= H e^{\\frac{t}{H}}$ where $B$ is a fractional Brownian motion with Hurst parameter $H \\in (0,1)$. In this article, in the case $H>1/2$, we prove that the least squares estimator $\\hat{\\theta}_T$ introduced in [\\cite{h-n}, Statist. Probab. Lett. 80, no. 11-12, 1030-1038], provides a consistent estimator. Moreover, using central limit theorem for multiple Wiener integrals, we prove asymptotic normality of the estimator valid for the whole range $H \\in(1/2,1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-25T10:57:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional ornstein-uhlenbeck process",
      "drift parameter estimation",
      "second kind",
      "fractional brownian motion",
      "central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.6047A"
    }
  }
}