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Weighted renewal functions: a hierarchical approach

Part of: Distribution theory - Probability Special processes Real functions

Published online by Cambridge University Press:  01 July 2016

Edward Omey  and
Jef L. Teugels
Edward Omey*
Affiliation:
Economische Hogeschool Sint-Aloysius
Jef L. Teugels*
Affiliation:
Katholieke Universiteit Leuven
*
∗ Postal address: Department of Mathematics and Statistics, Economische Hogeschool Sint-Aloysius, Stormstraat 2, 1000-Brussels, Belgium.
∗∗ Postal address: Katholieke Universiteit Leuven, Universitair Centrum Voor Statisiek, De Coylaan 52B, B3001 Heverlee, Belgium. Email address: [email protected]
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Abstract

We extend classical renewal theorems to the weighted case. A hierarchical chain of successive sharpenings of asymptotic statements on the weighted renewal functions is obtained by imposing stronger conditions on the weighting coefficients.

Keywords

Renewal theoryelementary renewal theoremBlackwell's theoremkey renewal theoremdirect Riemann integrabilityremainder theoremsrenewal moments

MSC classification

Primary: 60K05: Renewal theory
Secondary: 60E05: Distributions 60K10: Applications (reliability, demand theory, etc.) 26A12: Rate of growth of functions, orders of infinity, slowly varying functions
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 2 , June 2002 , pp. 394 - 415
Copyright
Copyright © Applied Probability Trust 2002 

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