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Transactions of the American Mathematical Society

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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: 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.


References [Enhancements On Off] (What's this?)

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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

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