{
  "id": "0804.0407",
  "version": "v1",
  "published": "2008-04-02T18:17:17.000Z",
  "updated": "2008-04-02T18:17:17.000Z",
  "title": "Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic Parabolic Equations with Additive Fractional Brownian Motion",
  "authors": [
    "Igor Cialenco",
    "Sergey Lototsky",
    "Jan Pospisil"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and fractional in time with the Hurst parameter $H\\geq 1/2$. The objective is to study asymptotic properties of the maximum likelihood estimator as the number of the Fourier coefficients increases. A necessary and sufficient condition for consistency and asymptotic normality is presented in terms of the eigenvalues of the operators in the equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-02T18:17:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "62F12"
    ],
    "keywords": [
      "additive fractional brownian motion",
      "maximum likelihood estimator",
      "stochastic parabolic equations",
      "asymptotic properties",
      "fourier coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.0407C"
    }
  }
}