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

Korshunov, Dmitry (2018) On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes. Stochastic Processes and their Applications, 128 (4). pp. 1316-1332. ISSN 0304-4149

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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.

Item Type:
Journal Article
Journal or Publication Title:
Stochastic Processes and their Applications
Additional Information:
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
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
ID Code:
87232
Deposited By:
Deposited On:
22 Aug 2017 15:44
Refereed?:
Yes
Published?:
Published
Last Modified:
27 Sep 2020 04:00