{
  "id": "1806.01487",
  "version": "v1",
  "published": "2018-06-05T04:10:08.000Z",
  "updated": "2018-06-05T04:10:08.000Z",
  "title": "Berry-Esseen bound for the Parameter Estimation of Fractional Ornstein-Uhlenbeck Processes",
  "authors": [
    "Yong Chen",
    "Nenghui Kuang",
    "Ying Li"
  ],
  "comment": "9 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "For the least squares estimator $\\hat{\\theta}$ for the drift parameter $\\theta$ of an Ornstein-Uhlenbeck process driven by fractional Brownian motion with Hurst index $H\\in [\\frac12,\\frac34]$, we show the Berry-Esseen bound of the Kolmogorov distance between Gaussian random variable and $\\sqrt{T}(\\hat{\\theta}_T-\\theta) $ with $H\\in[\\frac12,\\,\\frac34)$, ( $\\sqrt{\\frac{T}{\\log T}}(\\hat{\\theta}_T-\\theta)$ with $H=\\frac{3}{4}$ respectively) is $\\frac{1}{\\sqrt{T^{3-4H}}}$, ( $\\frac{1}{\\log T}$ respectively). The strategy is to exploit Corollary 1 of Kim and Park [Journal of Multivariate Analysis 155, P284-304.(2017)].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-05T04:10:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "60F25",
      "62M09"
    ],
    "keywords": [
      "fractional ornstein-uhlenbeck processes",
      "berry-esseen bound",
      "parameter estimation",
      "fractional brownian motion",
      "ornstein-uhlenbeck process driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}