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October, 1978 Limit Theorems for Semi-Markov Processes and Renewal Theory for Markov Chains
K. B. Athreya, D. McDonald, P. Ney
Ann. Probab. 6(5): 788-797 (October, 1978). DOI: 10.1214/aop/1176995429


With any Harris-recurrent Markov chain one can associate a sequence of random times at which the chain has the same distribution, and the chain can thereby be shown to be equivalent to one having a recurrence point. This idea makes available a regeneration scheme for such chains, which is exploited in this paper to prove the ergodic theorem for semi-Markov processes, and a renewal theorem for Markov chains on a general state space.


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K. B. Athreya. D. McDonald. P. Ney. "Limit Theorems for Semi-Markov Processes and Renewal Theory for Markov Chains." Ann. Probab. 6 (5) 788 - 797, October, 1978.


Published: October, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0397.60052
MathSciNet: MR503952
Digital Object Identifier: 10.1214/aop/1176995429

Primary: 60J10
Secondary: 60K15

Keywords: ergodic theorem , Markov chains , regeneration , Renewal theorem , semi-Markov process

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 5 • October, 1978
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