On the range of recurrent Markov chains

Athreya, K. B. (1985) On the range of recurrent Markov chains Statistics & Probability Letters, 3 (3). pp. 143-145. ISSN 0167-7152

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/016771...

Related URL: http://dx.doi.org/10.1016/0167-7152(85)90052-5


Let {Xn}0 be an irreducible recurrent Markov Chain on the nonnegative integers. A result of Chosid and Isaac (1978) gives a sufficient condition for n-1Rn → 0 w.p.1. where Rn is the range of the chain. We give an alternative proof using Kingman's subadditive ergodic theorem (Kingman, 1973). Some examples are also given.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Markov Chain; Recurrence; Range; Subadditive Ergodic Theorem
ID Code:1127
Deposited On:05 Oct 2010 12:53
Last Modified:12 May 2011 10:08

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