Uniform and ratio limit theorems for Markov renewal and semi-regenerative processes on a general state space
Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Volume 14 (1978) no. 2, pp. 119-143.
@article{AIHPB_1978__14_2_119_0,
     author = {Nummelin, E.},
     title = {Uniform and ratio limit theorems for {Markov} renewal and semi-regenerative processes on a general state space},
     journal = {Annales de l'institut Henri Poincar\'e. Section B. Calcul des probabilit\'es et statistiques},
     pages = {119--143},
     publisher = {Gauthier-Villars},
     volume = {14},
     number = {2},
     year = {1978},
     zbl = {0402.60087},
     mrnumber = {507729},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1978__14_2_119_0/}
}
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Nummelin, E. Uniform and ratio limit theorems for Markov renewal and semi-regenerative processes on a general state space. Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Volume 14 (1978) no. 2, pp. 119-143. http://www.numdam.org/item/AIHPB_1978__14_2_119_0/

[1] E. Arjas, E. Nummelin and R.L. Tweedie, Uniform limit theorems for non-singular renewal and Markov renewal processes. 1976. To appear in J. Appl. Prob. | MR | Zbl

[2] M.R. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory. Academic Press, New York, 1968. | MR | Zbl

[3] E. Cinlar, Periodicity in Markov renewal theory. Adv. Appl. Prob., t. 6, p. 61-78. | MR | Zbl

[4] R. Cogburn, A uniform theory for sums of Markov chain transition probabilities. Ann. Probability, t. 3, 1975, p. 191-214. | MR | Zbl

[5] J.L. Doob, Stochastic processes. Wiley and Sons, New York, 1953. | MR | Zbl

[6] M. Duflo and D. Revuz, Propriétés asymptotiques des probabilités de transition des processus de Markov récurrents. Ann. Inst. Henri Poincaré, Sect. B, t. V, 1969, p. 233-244. | Numdam | MR | Zbl

[7] J. Jacod, Théorème de renouvellement et classification pour les chaînes semi-markoviennes. Ann. Inst. Henri Poincaré, Sect. B, t. VII, 1971, p. 83-129. | Numdam | MR | Zbl

[8] J. Jacod, Corrections et compléments à l'article : « Théorème de renouvellement et classification pour les chaînes semi-markoviennes ». Ann. Inst. Henri Poincaré, Sect. B, t. X, 1974, p. 201-209. | Numdam | MR | Zbl

[9] H. Kesten, Renewal theory for functionals of a Markov chain with general state space. Ann. Probability, t. 2, 1974, p. 355-386. | MR | Zbl

[10] D. Mcdonald, On semi-Markov and semi-regenerative processes I. 1976, to appear. | MR | Zbl

[11] D. Mcdonald, On semi-Markov and semi-regenerative processes II. 1976, to appear. | MR | Zbl

[12] M. Métivier, Théorème limite quotient pour les chaînes de Markov récurrentes au sens de Harris. Ann. Inst. Henri Poincaré, Sect. B, t. VIII, 1972, p. 93-105. | EuDML | Numdam | MR | Zbl

[13] J. Neveu, Potentiel markovien récurrent des chaînes de Harris. Ann. Inst. Fourier, t. 22, 1972, p. 85-130. | EuDML | Numdam | MR | Zbl

[14] J. Neveu, Généralisation d'un théorème limite-quotient, in : Trans. 6th Prague Conf. on Inf. Theory, Stat. Dec. Funct., Random Proc. (Czech. Acad. Sci., Prague), 1973. | MR | Zbl

[15] E. Nummelin, A splitting technique for φ-recurrent Markov chains. 1976, to appear.

[16] E. Nummelin, On the Poisson equation for φ-recurrent Markov chains. Preprint, Helsinki University of Technology, 1976.

[17] S. Grey, Limit theorems for Markov chain transition probabilities. Van Nostrand, New York, 1971.

[18] R. Pyke and R. Schaufele, Limit theorems for Markov renewal processes. Ann. Math. Statist., t. 35, 1964, p. 1746-1764. | MR | Zbl

[19] D. Revuz, Markov chains. North-Holland, Amsterdam, 1975. | MR | Zbl