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

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

Journal

Stochastic Processes and their Applications
ISSN: 0304-4149

Output data

Year: 2024, Volume: 176, Article number : 104422, Pages count : 16 DOI: 10.1016/j.spa.2024.104422

Tags

Uniform asymptotics. Stopping time. Renewal process, Subexponential distribution, Lévy process, Random walk

Authors

Foss Sergey ^1,2 , Korshunov Dmitry ³ , Palmowski Zbigniew ⁴

Affiliations

1	Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK
2	Sobolev Institute of Mathematics, Novosibirsk, Russia
3	Department of Mathematics and Statistics, Lancaster University, UK
4	Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland

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 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 independent of the processes. We link our results with random walk theory.

Foss S. , Korshunov D. , Palmowski Z.
Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes
Stochastic Processes and their Applications. 2024. V.176. 104422 :1-16. DOI: 10.1016/j.spa.2024.104422 WOS Scopus РИНЦ OpenAlex

Submitted:	Mar 30, 2023
Accepted:	Jun 20, 2024
Published online:	Jun 25, 2024
Published print:	Sep 3, 2024

Web of science:	WOS:001285807300001
Scopus:	2-s2.0-85199885012
Elibrary:	68309374
OpenAlex:	W4399992950

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