On Two Recent Papers on Ergodicity in Nonhomogeneous Markov Chains

In [7] ergodic properties of nonhomogeneous denumerable state space Markov chains were studied. It was noticed in [6] that the results obtained in [7] were easily extended to arbitrary state spaces. However, it was admitted in [6] that the transition mechanism of the chain was defined by means of transition density functions, thus restricting the generality of the approach and, moreover, introducing elements irrelevant to the problem. The aim of this note is to draw attention to the fact that ergodic properties of the most general nonhomogeneous Markov chains are easily obtained by using a theory developed by Dobrusin [2] in the middle fifties.