Two-Sided Bounds on the Rate of Convergence for Continuous-Time finite Inhomogeneous Markov Chains

Abstract

We suggest an approach to obtaining general two-sided bounds on the rate of convergence in terms of special “weighted” norms related to total variation. Some important classes of continuous-time Markov chains are considered: birth-death-catastrophes processes, queueing models with batch arrivals and group services, chains with absorption in zero.

Keywords: continuous-time Markov chains, inhomogeneous Markov chains, ergodicity bounds, special norms.