International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 4, Pages 537-587

On the asymptotic events of a Markov chain

Harry Cohn

Department of Statistics, University of Melbourne, Parkville 3052, Victoria, Australia

Received 4 December 1978

Copyright © 1979 Harry Cohn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.