Two Examples of Parameter Estimation for Stochastic Partial Differential Equations

M. Hübner, R. Khasminskii and B. L. Rozovskii
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M. Hübner: University of Southern California, Department of Mathematics
R. Khasminskii: Institute for Problems of Information Transmission
B. L. Rozovskii: University of Southern California, Center for Applied Mathematical Sciences

A chapter in Stochastic Processes, 1993, pp 149-160 from Springer

Abstract: Abstract We study parameter estimation for two types of parabolic stochastic PDE’s. Examples considered in this article suggest that asymptotic properties of maximum likelihood estimators (MLE’s) for Galerkin approximations to these SPDE’s depend critically on certain properties of the distributions of solutions to the original equations. In particular, singularity of the distributions for different values of the parameter provides for consistency of the MLE as the dimension of the approximation approaches infinity.

Keywords: Maximum Likelihood Estimator; Covariance Operator; Wiener Process; Asymptotic Normality; Stochastic Integral (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-7909-0_18

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DOI: 10.1007/978-1-4615-7909-0_18

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