{
  "id": "1202.5061",
  "version": "v4",
  "published": "2012-02-22T23:04:01.000Z",
  "updated": "2013-07-16T09:45:46.000Z",
  "title": "Berry-Esséen bounds for the least squares estimator for discretely observed fractional Ornstein-Uhlenbeck processes",
  "authors": [
    "Khalifa Es-Sebaiy"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1102.5491",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\theta>0$. We consider a one-dimensional fractional Ornstein-Uhlenbeck process defined as $dX_t= -\\theta\\ X_t dt+dB_t,\\quad t\\geq0,$ where $B$ is a fractional Brownian motion of Hurst parameter $H\\in(1/2,1)$. We are interested in the problem of estimating the unknown parameter $\\theta$. For that purpose, we dispose of a discretized trajectory, observed at $n$ equidistant times $t_i=i\\Delta_{n}, i=0,...,n$, and $T_n=n\\Delta_{n}$ denotes the length of the `observation window'. We assume that $\\Delta_{n} \\rightarrow 0$ and $T_n\\rightarrow \\infty$ as $n\\rightarrow \\infty$. As an estimator of $\\theta$ we choose the least squares estimator (LSE) $\\hat{\\theta}_{n}$. The consistency of this estimator is established. Explicit bounds for the Kolmogorov distance, in the case when $H\\in(1/2,3/4)$, in the central limit theorem for the LSE $\\hat{\\theta}_{n}$ are obtained. These results hold without any kind of ergodicity on the process $X$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-07-16T09:45:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional ornstein-uhlenbeck processes",
      "squares estimator",
      "berry-esséen bounds",
      "one-dimensional fractional ornstein-uhlenbeck process",
      "fractional brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.5061E"
    }
  }
}