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Laplace transforms and the renewal equation

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  14 July 2016

Y. Kebir
Y. Kebir*
Affiliation:
Loyola University of Chicago
*
∗Postal address: Department of Mathematical Sciences, Loyola University of Chicago, Chicago, Illinois 60626, USA.
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Abstract

Vinogradov (1973) used the Laplace transform to characterize the IFR class of life distributions and later Block and Savits (1980) extended the characterization to the main reliability classes. Here we use the same transform again to characterize the continuous time renewal equation and some properties of its solution.

Keywords

LAPLACE TRANSFORMRENEWAL EQUATIONRENEWAL FUNCTIONNBUNWUDFRCONCAVITYLOGCONCAVITYCONVEXITYLOGCONVEXITYBROWN'S CONJECTURE

MSC classification

Primary: 60K05: Renewal theory
Secondary: 60E10: Characteristic functions; other transforms
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 395 - 403
Copyright
Copyright © Applied Probability Trust 1997 

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