Singularly perturbed Markov chains. I. Asymptotic properties

This work is concerned with singularly perturbed Markov chains. Its focus is on asymptotic properties, and applications for controlled dynamic systems. An integrated approach to continuous-time singularly perturbed Markov chains arising in many areas of endeavor is developed. Owing to the pervasive practical use of Markovian formulation in many applications, there is a resurgence of interest in studying further properties of the Markov chains. The article discusses asymptotic expansion. The models under consideration are in the form of singularly perturbed chains with weak and strong interactions. Structural properties of the underlying chains are investigated. Proofs are omitted for brevity