A new approach to the limit theory of recurrent Markov chains

Athreya, K. B. ; Ney, P. (1978) A new approach to the limit theory of recurrent Markov chains Transactions of the American Mathematical Society, 245 . pp. 493-501. ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/1978-245-00/S0002...

Related URL: http://dx.doi.org/10.1090/S0002-9947-1978-0511425-0

Abstract

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 {XN; 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.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
Keywords:Markov Chains; Regeneration; Ergodic Theorem; Invariant Measure
ID Code:1112
Deposited On:05 Oct 2010 12:54
Last Modified:16 May 2016 12:16

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