I. Fleischer et A. Joffe, RATIO ERGODICITY FOR NONHOMOGENEOUS MARKOV-CHAINS IN GENERAL STATE-SPACES, Journal of theoretical probability, 8(1), 1995, pp. 31-37
In Refs.7, 8, 12-14, applications of Birkhoff's coefficient of ergodic
ity to the study of products of finite and infinite matrices are given
. In this paper we intend to show that using the ideas and results of
Birkhoff((2)) and Bauer et. al.((1)) one can establish such results in
the general setting of positive operators on a space of measures and
in particular, in the study of nonhomogeneous Markov Chains in general
state spaces. In this setup the proofs are very simple. Since the hig
h level of generality in Ref, 1 hinders an easy understanding of the s
pecial case of interest to probabilists, we present a self-contained t
reatment. Even though our aim is methodological, our theorems are new,
even in the case of infinite matrices.