Lower bounds for the rate of convergence for continuous-time inhomogeneous Markov chains with a finite state space

An approach is proposed to the construction of general lower bounds for the rate of convergence of probability characteristics of continuous-time inhomogeneous Markov chains with a finite state space in terms of special “weighted” norms related to total variation. We study the sharpness of these bounds for finite birth–death–catastrophes process and for a Markov chain with large output intensity from a state. © 2018 Elsevier B.V.