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Tail probabilities for non-standard risk and queueing processes with subexponential jumps

  • Søren Asmussen (a1), Hanspeter Schmidli (a2) and Volker Schmidt (a3)

Abstract

A well-known result on the distribution tail of the maximum of a random walk with heavy-tailed increments is extended to more general stochastic processes. Results are given in different settings, involving, for example, stationary increments and regeneration. Several examples and counterexamples illustrate that the conditions of the theorems can easily be verified in practice and are in part necessary. The examples include superimposed renewal processes, Markovian arrival processes, semi-Markov input and Cox processes with piecewise constant intensities.

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Corresponding author

Postal address: Department of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden.
∗∗ Postal address: Institute of Mathematics, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark. Email address: schmidli@imf.au.dk
∗∗∗ Postal address: Institute of Stochastics, University of Ulm, D-89069 Ulm, Germany.

References

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Tail probabilities for non-standard risk and queueing processes with subexponential jumps

  • Søren Asmussen (a1), Hanspeter Schmidli (a2) and Volker Schmidt (a3)

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