{
  "id": "1102.5491",
  "version": "v1",
  "published": "2011-02-27T11:00:37.000Z",
  "updated": "2011-02-27T11:00:37.000Z",
  "title": "Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-ergodic Case",
  "authors": [
    "Rachid Belfadli",
    "Khalifa Es-Sebaiy",
    "Youssef Ouknine"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\\theta X_tdt+dB_t,\\ t\\geq0$, with a parameter $\\theta>0$, where $B$ is a fractional Brownian motion of Hurst index $H\\in(1/2,1)$. We study the consistency and the asymptotic distributions of the least squares estimator $\\hat{\\theta}_t$ of $\\theta$ based on the observation $\\{X_s,\\ s\\in[0,t]\\}$ as $t\\rightarrow\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-27T11:00:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62F12",
      "60G18",
      "60G15"
    ],
    "keywords": [
      "fractional ornstein-uhlenbeck processes",
      "non-ergodic case",
      "parameter estimation problem",
      "fractional brownian motion",
      "non-ergodic fractional ornstein-uhlenbeck process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.5491B"
    }
  }
}