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Tail Asymptotics of the Supremum of a Regenerative Process

  • Zbigniew Palmowski (a1) and Bert Zwart (a2)

Abstract

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.

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Copyright

Corresponding author

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

References

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Tail Asymptotics of the Supremum of a Regenerative Process

  • Zbigniew Palmowski (a1) and Bert Zwart (a2)

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