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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 journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>04/2018
<mark>Journal</mark>Stochastic Processes and their Applications
Issue number4
Volume128
Number of pages17
Pages (from-to)1316-1332
Publication StatusPublished
Early online date29/07/17
<mark>Original language</mark>English

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 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.

Bibliographic note

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