A new approach to the limit theory of recurrent Markov chains

Athreya, K. B.; Ney, P.

doi:10.1090/S0002-9947-1978-0511425-0

A new approach to the limit theory of recurrent Markov chains
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by K. B. Athreya and P. Ney

Trans. Amer. Math. Soc. 245 (1978), 493-501

DOI: https://doi.org/10.1090/S0002-9947-1978-0511425-0

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Abstract:

Let $\{ {X_n}; n \geqslant 0\}$ be a Harris-recurrent Markov chain on a general state space. It is shown that there is a sequence of random times $\{ {N_i}; i \geqslant 1\}$ such that $\{ {X_{{N_i}}};{\text { }}i \geqslant 1\}$ 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.

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