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

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Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes. / Foss, S.; Korshunov, D.; Palmowski, Z.
In: Stochastic Processes and their Applications, Vol. 176, 104422, 31.10.2024.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Foss, S, Korshunov, D & Palmowski, Z 2024, 'Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes', Stochastic Processes and their Applications, vol. 176, 104422. https://doi.org/10.1016/j.spa.2024.104422

APA

Foss, S., Korshunov, D., & Palmowski, Z. (2024). Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes. Stochastic Processes and their Applications, 176, Article 104422. https://doi.org/10.1016/j.spa.2024.104422

Vancouver

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 Oct 31;176:104422. Epub 2024 Jul 31. doi: 10.1016/j.spa.2024.104422

Author

Foss, S. ; Korshunov, D. ; Palmowski, Z. / Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes. In: Stochastic Processes and their Applications. 2024 ; Vol. 176.

Bibtex

@article{a73bf4d1345c497381d9d6fe1a36a47c,
title = "Maxima over random time intervals for heavy-tailed compound renewal and L{\'e}vy processes",
abstract = "We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a L{\'e}vy 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.",
author = "S. Foss and D. Korshunov and Z. Palmowski",
year = "2024",
month = oct,
day = "31",
doi = "10.1016/j.spa.2024.104422",
language = "English",
volume = "176",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes

AU - Foss, S.

AU - Korshunov, D.

AU - Palmowski, Z.

PY - 2024/10/31

Y1 - 2024/10/31

N2 - 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.

AB - 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.

U2 - 10.1016/j.spa.2024.104422

DO - 10.1016/j.spa.2024.104422

M3 - Journal article

VL - 176

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

M1 - 104422

ER -