On the mixing property and the ergodic principle for nonhomogeneous Markov chains

Abstract

We study different types of limit behavior of infinite dimension discrete time nonhomogeneous Markov chains. We show that the geometric structure of the set of those Markov chains which have asymptotically stationary density depends on the considered topologies. We generalize and correct some results from Ganikhodjaev et al. (2006) [3].