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

Dmitry Korshunov

Stochastic Processes and their Applications, 2018, vol. 128, issue 4, 1316-1332

Abstract: We study subexponential tail asymptotics for the distribution of the maximum Mt≔supu∈[0,t]Xu of a process Xt 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.

Keywords: Lévy process; Compound renewal process; Distribution tails; Heavy tails; Long-tailed distributions; Subexponential distributions; Random walk (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414917301813
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:4:p:1316-1332

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2017.07.013

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().