Uniformly Strong Ergodicity of Markov Chains in Random Environments

For Markov chains in random environments, Cogbum( 1984, 1990) first introduced weak ergodic concept that starting time is original point, and gave some conditions ensuring that the chains are weakly ergodic; Li Ying-qiu, Yan Xiao-bing, Wang He-song(2003) and LI Ying-qiu, YAN Xiao-bing and LI Ming-liang (2003) introduced uniformly weak ergodic and strong ergodic concept that starting time is any point, and gave some conditions ensuring that the chains are uniformly weakly ergodic or strongly ergodic. In term of above ideas, the definitions of uniformly strong ergodic and XN+-uniformly weak ergodic that starting time is any point are introduced. Some conditions ensuring that the chains are uniformly strongly ergodic are given. It is the basis of further research for Markov chains in random environments.