Poisson limit theorem for countable Markov chains in Markovian environments.
The authors consider a countable Markov chain in a (countable) random environment. Under suitable assumptions they prove a Poisson limit theorem for such a chain by using a Poisson limit theorem for 0-1 valued independent random variables, which is due to B. A. Sevast'yanov. The result obtained generalizes a Poisson limit theorem for finite Markov chains proved by \textit{B. Pitskel} [Ergodic Theory Dyn. Syst. 11, 501--513 (1991; Zbl 0753.60058)].
scientific article; zbMATH DE number 2029357