Limit Theorems for Semi-Markov Processes and Renewal Theory for Markov Chains
Open Access
- 1 October 1978
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 6 (5) , 788-797
- https://doi.org/10.1214/aop/1176995429
Abstract
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.Keywords
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