Foss, S. and Korshunov, D. and Palmowski, Z. (2024) Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes. Stochastic Processes and their Applications, 176: 104422. ISSN 0304-4149
Text (Levy_stopping_timever)
Levy_stopping_timever.pdf - Accepted Version
Available under License Creative Commons Attribution.
Download (352kB)
Levy_stopping_timever.pdf - Accepted Version
Available under License Creative Commons Attribution.
Download (352kB)
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.
Item Type:
Journal Article
Journal or Publication Title:
Stochastic Processes and their Applications
Uncontrolled Keywords:
Research Output Funding/no_not_funded
Subjects:
?? no - not fundednomodelling and simulationapplied mathematicsstatistics and probability ??
Departments:
ID Code:
223861
Deposited By:
Deposited On:
09 Sep 2024 14:50
Refereed?:
Yes
Published?:
Published
Last Modified:
18 Sep 2024 01:13