Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes

Sergey Foss, Dmitry Korshunov, Zbigniew Palmowski

Research output: Contribution to journalArticlepeer-review

Abstract

We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a Lévy process, both with negative drift, over random time horizon τ that does not depend on the future increments of the process. Our asymptotic results are uniform over the whole class of such random times. Particular examples are given by stopping times and by τ independent of the processes. We link our results with random walk theory.
Original languageEnglish
Article number104422
JournalStochastic Processes and their Applications
Early online date25 Jun 2024
DOIs
Publication statusE-pub ahead of print - 25 Jun 2024

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