RT Journal Article
T1 Sufficient conditions for regularity, positive recurrence, and absorption in level‐dependent QBD processes and related block‐structured Markov chains
A1 Gómez Corral, Antonio
A1 Langwade, Joshua
A1 López García, Martín
A1 Molina París, Carmen
AB 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.
PB Wiley
SN 0170-4214
YR 2022
FD 2022-12-09
LK https://hdl.handle.net/20.500.14352/72779
UL https://hdl.handle.net/20.500.14352/72779
LA eng
NO CRUE-CSIC (Acuerdos Transformativos 2022)
NO Ministerio de Ciencia e Innovación (MICINN)
NO K Ministry of Defence, Defence Science and Technology Laboratory (Dstl)
DS Docta Complutense
RD 21 abr 2025