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A Wavelet-Based Computational Framework for a Block-Structured Markov Chain with a Continuous Phase Variable

Author

Listed:
  • Shuxia Jiang

    (School of Traffic and Logistics, Central South University of Forestry and Technology, Changsha 410004, China)

  • Nian Liu

    (Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA)

  • Yuanyuan Liu

    (School of Mathematics and Statistics, HNP-LAMA, New Campus, Central South University, Changsha 410083, China)

Abstract

We consider the computing issues of the steady probabilities for block-structured discrete-time Markov chains that are of upper-Hessenberg or lower-Hessenberg transition kernels with a continuous phase set. An effective computational framework is proposed based on the wavelet transform, which extends and modifies the arguments in the literature for quasi-birth-death (QBD) processes. A numerical procedure is developed for computing the steady probabilities based on the fast discrete wavelet transform, and several examples are presented to illustrate its effectiveness.

Suggested Citation

  • Shuxia Jiang & Nian Liu & Yuanyuan Liu, 2023. "A Wavelet-Based Computational Framework for a Block-Structured Markov Chain with a Continuous Phase Variable," Mathematics, MDPI, vol. 11(7), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1587-:d:1106989
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    References listed on IDEAS

    as
    1. Jiang, Shuxia & Latouche, Guy & Liu, Yuanyuan, 2015. "Wavelet transform for quasi-birth–death process with a continuous phase set," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 354-376.
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    Cited by:

    1. Francisco Germán Badía & María D. Berrade, 2023. "Special Issue “Probability Theory and Stochastic Modeling with Applications”," Mathematics, MDPI, vol. 11(14), pages 1-3, July.

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