Conditions for strong ergodicity using intensity matrices

Abstract

Sufficient conditions for strong ergodicity of discrete-time non-homogeneous Markov chains have been given in several papers. Conditions have been given using the left eigenvectors ψ n of P n ( ψ n P n = ψ n ) and also using the limiting behavior of P n . In this paper we consider the analogous results in the case of continuous-time Markov chains where one uses the intensity matrices Q ( t ) instead of P ( s, t ). A bound on the rate of convergence of certain strongly ergodic chains is also given.