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Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence

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. 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
Related URLs:
URLURL TypeDescription
https://doi.org/10.12732/caa.v23i2.4DOIArticle
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6904110PubMed CentralArticle
https://arxiv.org/abs/1807.04904arXivDiscussion Paper
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).
Funders:
Funding AgencyGrant Number
NIHR21AA17711
NIHR01AA026368-01
Subject Keywords:distribution estimation, random parameters, distributed parameter systems, abstract parabolic systems, regularly dissipative operators
Issue or Number:2
PubMed Central ID:PMC6904110
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:13 Apr 2020 17:19

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