Asymptotic behaviour of Wiener-Hopf factors of a random walk

N. Veraverbeke

Stochastic Processes and their Applications, 1977, vol. 5, issue 1, 27-37

Abstract: For a random walk governed by a general distribution function F on (-[infinity], +[infinity]), we establish the exponential and subexponential asymptotic behaviour of the corresponding right Wiener-Hopf factor F+. The results apply to classes of distribution functions in recent publications: the subexponential class and a related (exponential) class [gamma]. Given the behaviour of F+, the Wiener-Hopf identity is used, to obtain the behaviour of F. To reverse the argument, we derive a new identity, similar in form to the first one. The results for F+ are then fruitfully applied to give a full description of the tail behaviour of the maximum of the randon walk. Also they provide new proofs for recent theorems on the tail of the waiting-time distribution in the GI/G/1 queue.

Keywords: Random; walk; Wiener-Hopffactorization; maximum-distribution; subexponential; GI/G/1; queue; distribution; functions (search for similar items in EconPapers)
Date: 1977
References: Add references at CitEc
Citations: View citations in EconPapers (25)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(77)90047-3
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:5:y:1977:i:1:p:27-37

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

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 ().