{
  "id": "1805.11747",
  "version": "v1",
  "published": "2018-05-29T23:53:40.000Z",
  "updated": "2018-05-29T23:53:40.000Z",
  "title": "Bayesian Estimations for Diagonalizable Bilinear SPDEs",
  "authors": [
    "Ziteng Cheng",
    "Igor Cialenco",
    "Ruoting Gong"
  ],
  "categories": [
    "math.ST",
    "math.PR",
    "stat.TH"
  ],
  "abstract": "The main goal of this paper is to study the parameter estimation problem, using the Bayesian methodology, for the drift coefficient of some linear (parabolic) SPDEs driven by a multiplicative noise of special structure. We take the spectral approach by assuming that one path of the first $N$ Fourier modes of the solution are continuously observed over a finite time interval. We derive Bayesian type estimators for the drift coefficient, and as custom for Bayesian statistics, we prove a Bernstein-Von Mises theorem for the posterior density. Consequently, we obtain some asymptotic properties of the proposed estimators, as $N\\to\\infty$. Finally, we present some numerical examples that illustrate the obtained theoretical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-29T23:53:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "65L09",
      "62M99"
    ],
    "keywords": [
      "diagonalizable bilinear spdes",
      "bayesian estimations",
      "drift coefficient",
      "parameter estimation problem",
      "finite time interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}