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Theory of semiregenerative phenomena

Published online by Cambridge University Press:  14 July 2016

N. U. Prabhu
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Abstract

We develop a theory of semiregenerative phenomena. These may be viewed as a family of linked regenerative phenomena, for which Kingman [6], [7] developed a theory within the framework of quasi-Markov chains. We use a different approach and explore the correspondence between semiregenerative sets and the range of a Markov subordinator with a unit drift (or a Markov renewal process in the discrete-time case). We use techniques based on results from Markov renewal theory.

Keywords

SEMIREGENERATIVE PHENOMENA AND SETSLINKED REGENERATIVE PHENOMENA: QUASI-MARKOV CHAINSSTANDARD PHENOMENASTABLE STATESLIFETIMEMARKOV RENEWAL PROCESSESMARKOV ADDITIVE PROCESSES
Type
Part 6 - The Analysis of Stochastic Phenomena
Information
Journal of Applied Probability , Volume 25 , Issue A , 1988 , pp. 257 - 274
Copyright
Copyright © Applied Probability Trust 1988 

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References

[1] Bondesson, L. (1981) On occupation times for quasi-Markov processes. J. Appl. Prob. 18, 297–301.CrossRefGoogle Scholar
[2] Çinlar, E. (1972) Markov additive processes. I. Z. Wahrscheinlichkeitsth. 24, 53–89.Google Scholar
[3] Çinlar, E. (1972) Markov additive processes. II. Z. Wahrscheinlichkeitsth. 24, 95–121.CrossRefGoogle Scholar
[4] Çinlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs. NJ.Google Scholar
[5] Feller, W. (1967) An Introduction to Probability Theory and its Applications, Vol. 1, 3rd edn. Wiley, New York.Google Scholar
[6] Kingman, J. F. C. (1965) Linked systems of regenerative events. Proc. London Math. Soc. 15, 125–150.CrossRefGoogle Scholar
[7] Kingman, J. F. C. (1972) Regenerative Phenomena, Wiley, New York.Google Scholar
[8] Kulkarni, V. G. and Prabhu, N. U. (1984) A fluctuation theory for Markov chains. Stoch. Proc. Appl. 16, 39–54.Google Scholar
[9] Neveu, J. (1961) Une généralisation des processus à acroissements positifs indépendents. Abh. Math. Sem. Univ. Hamburg 25, 36–61.CrossRefGoogle Scholar
[10] Prabhu, N. U. (1985) Wiener–Hopf factorization of Markov semigroups—I. The countable state space case. Proc. Seventh Conf. Probability Theory, ed. Iosifescu, M., VNU Science Press, Utrecht, 315–324.Google Scholar