On The Limit Theorems For Markov Chains In Random Environments

This paper was divided into two parts. In the first chapter, the existence of Markov chains in random environments was described, and their properties were studied. The Markov bichains was constructed. Moreover, some sufficient conditions for the strong law of large numbers for function of Markov chains in random environments were given. A function central limit theorem was established for Markov chains in random environments under the assumption that Markov bichains was stationary and ergodic. In second chapter, some limit theorems for function of countable Markov chains in Markovian environments were obtained, at the same time, some sufficient conditions on the jointly Markov chains and sample function of the jointly Markov chains were given.