A formulation of a Markov chain in a stationary random environment is given, and for the case of finite state space, necessary and sufficient conditions are found under which a state of the chain is inessential, positively essential or properly essential. It is shown that in this case improperly essential states cannot exist.
"Finite Markov Chains in Stationary Random Environments." Ann. Probab. 10 (4) 1041 - 1046, November, 1982. https://doi.org/10.1214/aop/1176993725