Bayesian Estimations for Diagonalizable Bilinear SPDEs

Ziteng Cheng, Igor Cialenco, Ruoting Gong

Published 2018-05-29Version 1

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.