A unified perturbation analysis framework for countable Markov chains

In this paper, we are devoted to singular perturbation analysis for discrete-time or continuous-time Markov chains. We modify and extend the drift condition method, well known for regular perturbation, to develop a new framework for singular perturbation analysis. Our results extend and improve the corresponding ones in [2] for singularly perturbed Markov chains by allowing a general perturbation form, less restrictive conditions, and more computable bounds. Our analysis covers the regular perturbation analysis, and hence unifies singular and regular perturbation analysis. Furthermore, our results are illustrated by two two-dimensional Markov chains, including a discrete-time queue and a continuous-time level dependent quasi-birth-death process.