Gómez Corral, AntonioLangwade, JoshuaLópez García, MartínMolina París, Carmen2023-06-222023-06-222022-12-090170-421410.1002/mma.8938https://hdl.handle.net/20.500.14352/72779CRUE-CSIC (Acuerdos Transformativos 2022)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.engAtribución-NoComercial-SinDerivadas 3.0 Españahttps://creativecommons.org/licenses/by-nc-nd/3.0/es/journal articlehttps://doi.org/10.1002/mma.8938https://onlinelibrary.wiley.com/doi/10.1002/mma.8938open accessabsorptionbirth-death processblock-structured Markov chainlevel-dependent quasi-birth-deathprocessrecurrenceregularityMatemáticas (Matemáticas)Estadística aplicada12 Matemáticas