A New Approach to the Limit Theory of Recurrent Markov Chains

Let \ Xₙ; n 0\ be a Harris-recurrent Markov chain on a general state space. It is shown that there is a sequence of random times \ Nᵢ; i 1\ such that \ X_Nᵢ; i 1\ are independent and identically distributed. This idea is used to show that \ Xₙ\ 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.