Limit Theorems for Semi-Markov Processes and Renewal Theory for Markov Chains
Athreya, K. B. ; McDonald, D. ; Ney, P.
Ann. Probab., Tome 6 (1978) no. 6, p. 788-797 / Harvested from Project Euclid
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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.
Publié le : 1978-10-14
Classification:  Markov chains,  semi-Markov process,  ergodic theorem,  renewal theorem,  regeneration,  60J10,  60K15 
@article{1176995429,
     author = {Athreya, K. B. and McDonald, D. and Ney, P.},
     title = {Limit Theorems for Semi-Markov Processes and Renewal Theory for Markov Chains},
     journal = {Ann. Probab.},
     volume = {6},
     number = {6},
     year = {1978},
     pages = { 788-797},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995429}
}

Athreya, K. B.; McDonald, D.; Ney, P. Limit Theorems for Semi-Markov Processes and Renewal Theory for Markov Chains. Ann. Probab., Tome 6 (1978) no. 6, pp.  788-797. http://gdmltest.u-ga.fr/item/1176995429/