ISSN:
1572-9036
Keywords:
60K05
;
60K15
;
60J15
;
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
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00994266
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