Quasi-ergodicity for non-homogeneous continuous-time Markov chains

The paper considers a non-homogeneous continuous-time Markov chain X(t) with countable state space. Definitions of uniform and strong quasi-ergodicity are introduced. The forward Kolmogorov system for X(t) is considered as a differential equation in the space of sequences l1. Sufficient conditions for uniform quasi-ergodicity are deduced from this equation. The paper considers conditions of uniform and strong ergodicity in the case of proportional intensities.