The Stationary Distribution of Markov Chains in Random Environments

In this paper, the concept of stationary distribution of Markov chains in random environments (MCIRE) is introduced, and basic properties of MCIRE are discussed. It is shown that there exists a stationary distribution of MCIRE under some natural conditions. In particular, the existence of stationary distribution of Cogburn's chain are discussed. Moreover, we give an example of MCIRE which stationary distribution exists.