International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 365-370
Non-homogeneous Markov chains with a finite state space and a Doeblin type theorem
Department of Mathematics, Eastern Michigan University, Ypsilanti 48197, MI, USA
Received 4 December 1992; Revised 4 March 1994
Copyright © 1995 Rita Chattopadhyay. 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.
Doeblin  considered some classes of finite state nonhomogeneous Markov chains
and studied their asymptotic behavior. Later Cohn  considered another class of such Markov
chains (not covered earlier) and obtained Doeblin type results. Though this paper does not
present the best possible results, the method of proof will be of interest to the reader. It is
elementary and based on Hajnal's results on products of nonnegative matrices.