%0 Journal Article
%A Gómez Corral, Antonio
%A Langwade, Joshua
%A López García, Martín
%A Molina París, Carmen
%T Sufficient conditions for regularity, positive recurrence, and absorption in level‐dependent QBD processes and related block‐structured Markov chains
%D 2022
%@ 0170-4214
%U https://hdl.handle.net/20.500.14352/72779
%X 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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