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    Weak Convergence of Hybrid Filtering Problems Involving Nearly Completely Decomposable Hidden Markov Chains


    Yin, G. and Dey, Subhrakanti (2003) Weak Convergence of Hybrid Filtering Problems Involving Nearly Completely Decomposable Hidden Markov Chains. SIAM Journal on Control and Optimization, 41 (6). pp. 1820-1842. ISSN 1095-7138

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    Abstract

    Concentrating on a class of hybrid discrete-time filtering problems that are modulated by a Markov chain, this work aims to reduce the complexity of the underlying problems. Since the Markov chain has a large state space, the solution of the problem relies on solving a large number of filtering equations. Exploiting the hierarchical structure of the system, it is noted that the transition probability matrix of the Markov chain can be viewed as a nearly decomposable one. It is shown that a reduced system of filtering equations can be obtained by aggregating the states of each recurrent class into one state. Extensions to inclusion of transient states and nonstationary cases are also treated.

    Item Type: Article
    Additional Information: Cite as: G. Yin and S. Dey. 2002. Weak Convergence of Hybrid Filtering Problems Involving Nearly Completely Decomposable Hidden Markov Chains. SIAM J. Control Optim. 41, 6 (2002), 1820–1842. DOI:https://doi.org/10.1137/S0363012901388464
    Keywords: Markov chain; filtering; near complete decomposability; weak convergence;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 14460
    Identification Number: https://doi.org/10.1137/S0363012901388464
    Depositing User: Subhrakanti Dey
    Date Deposited: 25 May 2021 14:14
    Journal or Publication Title: SIAM Journal on Control and Optimization
    Publisher: Society for Industrial and Applied Mathematics
    Refereed: Yes
    URI:

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