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Tail Asymptotics of the Supremum of a Regenerative Process

Part of: Applications Limit theorems Special processes

Published online by Cambridge University Press:  14 July 2016

Zbigniew Palmowski  and
Bert Zwart
Zbigniew Palmowski*
Affiliation:
Utrecht University and University of Wrocław
Bert Zwart*
Affiliation:
Georgia Institute of Technology
*
∗ Postal address: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland. Email address: zpalma@math.uni.wroc.pl
∗∗ Postal address: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA 30332-0205, USA. Email address: bertzwart@gatech.edu
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Abstract

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We give precise asymptotic estimates of the tail behavior of the distribution of the supremum of a process with regenerative increments. Our results cover four qualitatively different regimes involving both light tails and heavy tails, and are illustrated with examples arising in queueing theory and insurance risk.

Keywords

Cramér conditionfluid modelperturbed random walkregenerative processruin probability

MSC classification

Primary: 60F10: Large deviations 60K25: Queueing theory 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 349 - 365
Copyright
Copyright © Applied Probability Trust 2007 

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