A new approach to the limit theory of recurrent Markov chains

Authors:
K. B. Athreya and P. Ney

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

MSC:
Primary 60J10; Secondary 60K05

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

MathSciNet review:
511425

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Harris-recurrent Markov chain on a general state space. It is shown that there is a sequence of random times such that are independent and identically distributed. This idea is used to show that 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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Additional Information

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

Keywords:
Markov chains,
regeneration,
ergodic theorem,
invariant measure

Article copyright:
© Copyright 1978
American Mathematical Society