On the Ergodic Theory of Markov Chains

This paper presents results in the ergodic theory of Markov chains that are useful in certain cases where the well known theory of Foster and Pakes is not applicable. The paper gives the background leading to the results, describes their significance, proves two theorems, and presents an example. The conditions for ergodicity are based on the notion of conditional single transition displacement of a Markov chain due to Pakes.