Non-homogeneous Markov chains with a finite state space and a Doeblin type theorem (Q1805138)

Summary: \textit{W. Doeblin} [Publ. Fac. Sci. Univ. Masaryk 236, 3-13 (1937; Zbl 0016.41102)] considered some classes of finite state nonhomogeneous Markov chains and studied their asymptotic behavior. Later \textit{H. Cohn} [Adv. Appl. Probab. 13, 388-401 (1981; Zbl 0469.60065)] 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 \textit{J. Hajnal}'s results on products of nonnegative matrices [Math. Proc. Cambridge Philos. Soc. 79, 521-530 (1976; Zbl 0333.15013)].