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

Shuxia Jiang, Nian Liu and Yuanyuan Liu ()
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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

Mathematics, 2023, vol. 11, issue 7, 1-18

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.

Keywords: Markov chains; stationary distribution; wavelet transform; numerical algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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