The ergodic properties of Markov chains in random environments

For Markov chains in random environments,Li Ying-qiu(2003,2004) introduced the concepts of weak ergodicity,uniformly weak ergodicity,strong ergodicity,uniformly strong ergodicity of Markov chains in double infinitely random environments when the starting time is arbitrarily given point.Based on above results,all kinds of relationships among these ergodicities are discussed,and that θ→-chains is weak ergodicity if P(θ) limited to inevitable exit sets can be proved.