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International Journal of Mathematics and Mathematical Sciences
Volume 18, 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 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.


Doeblin [1] considered some classes of finite state nonhomogeneous Markov chains and studied their asymptotic behavior. Later Cohn [2] 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.