Finitely additive Markov chains

Abstract

In this paper we develop the theory of Markov chains with stationary transition probabilities, where the transition probabilities and the initial distribution are assumed only to be finitely additive.We prove a strong law of large numbers for recurrent chains.The problem of existence and uniqueness of finitely additive stationary initial distributions is studied and the ergodicity of recurrent chains under a stationary initial distribution is proved.