Sufficient conditions for regularity, positive recurrence, and absorption in level‐dependent QBD processes and related block‐structured Markov chains
This paper is concerned with level-dependent quasi-birth-death (LD-QBD) processes, i.e., multi-variate Markov chains with a block-tridiagonal -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...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/72779 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/72779 |
| Access Level: | acceso abierto |
| Palavra-chave: | absorption birth-death process block-structured Markov chain level-dependent quasi-birth-deathprocess recurrence regularity Matemáticas (Matemáticas) Estadística aplicada 12 Matemáticas |
| Resumo: | This paper is concerned with level-dependent quasi-birth-death (LD-QBD) processes, i.e., multi-variate Markov chains with a block-tridiagonal -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. |
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