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    Rights statement: This is the author’s version of a work that was accepted for publication in Stochastic Processes and their Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Stochastic Processes and their Applications, 128, (4), 2018 DOI: 10.1016/j.spa.2017.07.013

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On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes

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

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On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes. / Korshunov, Dmitry.
In: Stochastic Processes and their Applications, Vol. 128, No. 4, 04.2018, p. 1316-1332.

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

Harvard

Korshunov, D 2018, 'On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes', Stochastic Processes and their Applications, vol. 128, no. 4, pp. 1316-1332. https://doi.org/10.1016/j.spa.2017.07.013

APA

Korshunov, D. (2018). On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes. Stochastic Processes and their Applications, 128(4), 1316-1332. https://doi.org/10.1016/j.spa.2017.07.013

Vancouver

Korshunov D. On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes. Stochastic Processes and their Applications. 2018 Apr;128(4):1316-1332. Epub 2017 Jul 29. doi: 10.1016/j.spa.2017.07.013

Author

Korshunov, Dmitry. / On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes. In: Stochastic Processes and their Applications. 2018 ; Vol. 128, No. 4. pp. 1316-1332.

Bibtex

@article{2992ddeb487347f29df3ca0776bc722d,
title = "On subexponential tails for the maxima of negatively driven compound renewal and L{\'e}vy processes",
abstract = "We study subexponential tail asymptotics for the distribution of the maximum M t ≔ sup u ∈ [ 0 , t ] X u of a process X t with negative drift for the entire range of t > 0 . We consider compound renewal processes with linear drift and L{\'e}vy processes. For both processes we also formulate and prove the principle of a single big jump for their maxima. The class of compound renewal processes with drift particularly includes the Cram{\'e}r–Lundberg renewal risk process.",
keywords = "L{\'e}vy process, Compound renewal process, Distribution tails, Heavy tails, Long-tailed distributions, Subexponential distributions, Random walk",
author = "Dmitry Korshunov",
note = "This is the author{\textquoteright}s version of a work that was accepted for publication in Stochastic Processes and their Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Stochastic Processes and their Applications, 128, (4), 2018 DOI: 10.1016/j.spa.2017.07.013",
year = "2018",
month = apr,
doi = "10.1016/j.spa.2017.07.013",
language = "English",
volume = "128",
pages = "1316--1332",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",
number = "4",

}

RIS

TY - JOUR

T1 - On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes

AU - Korshunov, Dmitry

N1 - This is the author’s version of a work that was accepted for publication in Stochastic Processes and their Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Stochastic Processes and their Applications, 128, (4), 2018 DOI: 10.1016/j.spa.2017.07.013

PY - 2018/4

Y1 - 2018/4

N2 - We study subexponential tail asymptotics for the distribution of the maximum M t ≔ sup u ∈ [ 0 , t ] X u of a process X t with negative drift for the entire range of t > 0 . We consider compound renewal processes with linear drift and Lévy processes. For both processes we also formulate and prove the principle of a single big jump for their maxima. The class of compound renewal processes with drift particularly includes the Cramér–Lundberg renewal risk process.

AB - We study subexponential tail asymptotics for the distribution of the maximum M t ≔ sup u ∈ [ 0 , t ] X u of a process X t with negative drift for the entire range of t > 0 . We consider compound renewal processes with linear drift and Lévy processes. For both processes we also formulate and prove the principle of a single big jump for their maxima. The class of compound renewal processes with drift particularly includes the Cramér–Lundberg renewal risk process.

KW - Lévy process

KW - Compound renewal process

KW - Distribution tails

KW - Heavy tails

KW - Long-tailed distributions

KW - Subexponential distributions

KW - Random walk

U2 - 10.1016/j.spa.2017.07.013

DO - 10.1016/j.spa.2017.07.013

M3 - Journal article

VL - 128

SP - 1316

EP - 1332

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 4

ER -