Two classification theorems of states of Markov chains
C. W. Kim · Journal of Applied Probability · 1970
Summary Two theorems on Markov chains, both of which already appear in the literature: the classification of the states into the set of all non-recurrent (transient) states and recurrent classes, and the corresponding classification for idempotent Markov chains due to Doob, are proved from the viewpoint of ergodic theory.