International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 4, Pages 537-587
doi:10.1155/S0161171279000430

On the asymptotic events of a Markov chain

Abstract

In this paper we investigate some structure properties of the tail σ-field and the invariant σ-field of both homogeneous and nonhomogeneous Markov chains as representations for asymptotic events, descriptions of completely nonatomic and atomic sets and global characterizations of asymptotic σ-fields. It is shown that the Martin boundary theory can provide a unified approach to the asymptotic σ-fields theory.