The Annals of Probability · 1978 · 118 citations · 8 references
Natural SciencesMathematicsDynamical SystemsProbability TheoryStochastic ProcessesErgodic TheoryLimit TheoremsMarkov ChainsMarkov ProcessesRenewal TheorySemi-markov ProcessesErgodic ProcessesHarris RecurrenceLimit Theorems For Markov ChainsRenewal Theory Limit Theorems
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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