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.
- Finitely additive probabilities
- Markov chain
- Markov strategy
- Stationary initial distribution
- Stationary transition
ASJC Scopus subject areas
- Applied Mathematics