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Limit theorems for alternating renewal processes in the infinite mean case

Part of: Special processes

Published online by Cambridge University Press:  19 February 2016

K. V. Mitov  and
N. M. Yanev
K. V. Mitov*
Affiliation:
Bulgarian Academy of Sciences
N. M. Yanev*
Affiliation:
Bulgarian Academy of Sciences
*
∗ Postal address: Department of Probability and Statistics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev Street, 1113 Sofia, Bulgaria.
∗ Postal address: Department of Probability and Statistics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev Street, 1113 Sofia, Bulgaria.
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Abstract

The asymptotic behaviour of an occupation-time process associated with alternating renewal processes is investigated in the infinite mean cycle case. The limit theorems obtained extend some asymptotic results proved by Dynkin (1955), Lamperti (1958) and Erickson (1970) for the classical spent lifetime process. Some new phenomena are also presented.

Keywords

Alternating renewal processesstable lawsspent timelimiting distributions

MSC classification

Primary: 60K05: Renewal theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 4 , December 2001 , pp. 896 - 911
Copyright
Copyright © Applied Probability Trust 2001 

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Footnotes

This paper is supported by NFSI-Bulgaria, Grant No. MM 704/97.

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