A Poisson limit theorem for a strongly ergodic non-homogeneousMarkov chain ✩

A strongly ergodic non-homogeneous Markov chain is considered in the paper. As an analog of the Poisson limit theorem for a homogeneous Markov chain recurring to small cylindrical sets, a Poisson limit theorem is given for the non-homogeneous Markov chain. Meanwhile, some interesting results about approximation independence and probabilities of small cylindrical sets are given.  2003 Elsevier Science (USA). All rights reserved.