International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1979 / Article

Open Access

Volume 2 |Article ID 476427 | https://doi.org/10.1155/S0161171279000430

Harry Cohn, "On the asymptotic events of a Markov chain", International Journal of Mathematics and Mathematical Sciences, vol. 2, Article ID 476427, 51 pages, 1979. https://doi.org/10.1155/S0161171279000430

On the asymptotic events of a Markov chain

Received04 Dec 1978

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.

Copyright © 1979 Hindawi Publishing Corporation. 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.


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