Publication TypeJournal Article
Year of Publication2019
Start Page287
Date Published01/2019
AMSabstract parabolic systems, distributed parameter systems, distribution estimation, random parameters, regularly dissipative operators

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed.

Refereed DesignationRefereed
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Editorial Remark. The originally published version of the article has been revised on 2019-01-22: Reason (author's request): Not correct or not full author's address. The original published version is available from here.