On the maximal distance between two renewal epochs

P. Révész and E. Willekens

Stochastic Processes and their Applications, 1987, vol. 27, 21-41

Abstract: Let X1, X2... be a sequence of positive, independent, identically distributed (i.i.d.) random variables with S0 = 0, Sn = X1 + ... + Xn, n [greater-or-equal, slanted] 1. Denote by [tau]i = sup{nSn [less-than-or-equals, slant] t }. In this paper we establish almost sure lower and upper bounds for Mt = max{X1, X2,..., X[tau]t, t -S[tau]t} if the underlying distribution function has a regularly varying tail.

Keywords: renewal; processes; almost; sure; limit; laws (search for similar items in EconPapers)
Date: 1987
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(87)90003-2
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:27:y:1987:i::p:21-41

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 ().