Perturbation analysis in finite LD-QBD processes and applications to epidemic models.

ABSTRACT: In this paper, we adapt arguments from the paper by Caswell [11] to level-dependent quasi-birth-and-death (LD-QBD) processes, which constitute a wide class of structured Markov chains. A LD-QBD process has the special feature that its space of states can be structured by levels (groups of states), so that a tridiagonal-by-blocks structure is obtained for its infinitesimal generator. For these processes, a number of algorithmic procedures exist in the literature in order to compute several performance measures while exploiting the underlying matrix structure; among others, these measures are related to first-passage times to a certain level L(0) and hitting probabilities at this level, the maximum level visited by the process before reaching states of level L(0), and the stationary distribu

SUBMITTER: Gomez-Corral A 

PROVIDER: S-EPMC6218010 | biostudies-literature | 2018 Oct

REPOSITORIES: biostudies-literature