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 language | English |
---|---|
Article number | 104422 |
Journal | Stochastic Processes and their Applications |
Volume | 176 |
Early online date | 25 Jun 2024 |
DOIs | |
Publication status | Published - Oct 2024 |
Keywords
- Lévy process
- Random walk
- Renewal process
- Stopping time
- Subexponential distribution
- Uniform asymptotics
ASJC Scopus subject areas
- Applied Mathematics
- Statistics and Probability
- Modelling and Simulation