The Strong Law of Large Numbers for Markov Chains in Markovian Environments

In this paper,a strong law of large numbers for funct io n of countable Markov chains in Markovian environments are investigated.Moreover ,some sufficient conditions on the jointly Markov chains and sample function of the jointly Markov chains are given.At last,R θchains are systematically studied,some sufficient conditions for the strong law of large numbers to hold for function of Markov chains in Markovian environments are obtained.