On the maximal distance between two renewal epochs

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.

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Year of publication:	1987
Authors:	Révész, P. ; Willekens, E.
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 27.1987, p. 21-41
Publisher:	Elsevier
Keywords:	renewal processes almost sure limit laws

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008872724