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Bayesian Estimations for Diagonalizable Bilinear SPDEs

by   Ziteng Cheng, et al.
Illinois Institute of Technology

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→∞. Finally, we present some numerical examples that illustrate the obtained theoretical results.


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