Sirlanci, Melike and Luczak, Susan E. and Rosen, I. G. (2019) Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence. Communications in Applied Analysis, 23 (2). pp. 287-329. ISSN 1083-2564. PMCID PMC6904110. doi:10.12732/caa.v23i2.4. https://resolver.caltech.edu/CaltechAUTHORS:20200103-135010143
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Abstract
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.
Item Type: | Article | ||||||||||||
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Additional Information: | © 2019 Dynamic Publishers, Inc., Acad. Publishers, Ltd. Received: December 6, 2018; Accepted: January 11, 2019; Published: January 22, 2019. This research was supported in part by grants R21AA17711 and R01AA026368-01 from the National Institute of Alcohol Abuse and Alcoholism (NIAAA). | ||||||||||||
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Subject Keywords: | distribution estimation, random parameters, distributed parameter systems, abstract parabolic systems, regularly dissipative operators | ||||||||||||
Issue or Number: | 2 | ||||||||||||
PubMed Central ID: | PMC6904110 | ||||||||||||
DOI: | 10.12732/caa.v23i2.4 | ||||||||||||
Record Number: | CaltechAUTHORS:20200103-135010143 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200103-135010143 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 100509 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 04 Jan 2020 23:56 | ||||||||||||
Last Modified: | 16 Nov 2021 17:54 |
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