A new approach to the limit theory of recurrent Markov chains

Abstract

Let {X_n; n ≥ 0} be a Harris-recurrent Markov chain on a general state space. It is shown that there is a sequence of random times {N_i; i ≥ 1} such that {X_N; i ≥ 1} are independent and identically distributed. This idea is used to show that {X_n} is equivalent to a process having a recurrence point, and to develop a regenerative scheme which leads to simple proofs of the ergodic theorem, existence and uniqueness of stationary measures.