Gómez-Corral, A, Langwade, J, Lopez Garcia, M orcid.org/0000-0003-3833-8595 et al. (1 more author) (2023) Sufficient conditions for regularity, positive recurrence and absorption in level-dependent QBD processes and related block-structured Markov chains. Mathematical Methods in the Applied Sciences, 46 (6). pp. 6756-6766. ISSN 0170-4214
Abstract
This paper is concerned with level-dependent quasi-birth-death (LD-QBD) processes, i.e., multi-variate Markov chains with a block-tridiagonal q-matrix, and a more general class of block-structured Markov chains, which can be seen as LD-QBD processes with total catastrophes. Arguments from univariate birth-death processes are combined with existing matrix-analytic formulations to obtain sufficient conditions for these block-structured processes to be regular, positive recurrent, and absorbed with certainty in a finite mean time. Specifically, it is our purpose to show that, as is the case for competition processes, these sufficient conditions are inherently linked to a suitably defined birth-death process. Our results are exemplified with two Markov chain models: a study of target cells and viral dynamics and one of kinetic proof-reading in T cell receptor signal transduction.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. |
Keywords: | absorption, birth-death process, block-structured Markov chain, level-dependent quasi-birth-death process, recurrence, regularity |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Dec 2022 15:43 |
Last Modified: | 26 Jul 2023 13:21 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1002/mma.8938 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:193974 |