A Wavelet-Based Computational Framework for a Block-Structured Markov Chain with a Continuous Phase Variable
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 extend...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/7/1587 |
| Summary: | 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. |
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| ISSN: | 2227-7390 |