Acta Applicandae Mathematica

, Volume 34, Issue 1–2, pp 213–223 | Cite as

Further results for semiregenerative phenomena

  • N. U. Prabhu
Part III: Regeneration
  • 24 Downloads

Abstract

A theory of semiregenerative phenomena was developed by the author. The set of points at which such a phenomenon occurs is called a semi regenerative set. There is a correspondence between a semiregenerative set and the range of a Markov subordinator with a unit drift (or a Markov renewal process in the discrete time case). Prabhu, Tang, and Zhu showed that the properties of semiregenerative sets associated with Markov random walks completely characterize the fluctuation behaviour of these processes in the nondegenerate case and also established a Wiener-Hopf factorization based on these sets. These results are surveyed in this paper.

Mathematics Subject Classifications (1991)

60K05 60K15 60J15 

Key words

Borel measures fluctuation behaviour linked regenerative phenomena Markov-additive process Markov random walk Markov renewal process quasi-Markov chain recurrent and regenerative phenomena semiregenerative phenomena semiregenerative sets subordinator Wiener-Hopf factorization 

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • N. U. Prabhu
    • 1
  1. 1.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA

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