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Renewal theory in two dimensions: Basic results

Published online by Cambridge University Press:  01 July 2016

Jeffrey J. Hunter
Jeffrey J. Hunter*
Affiliation:
University of Auckland, New Zealand
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Abstract

In this paper a unified theory for studying renewal processes in two dimensions is developed. Bivariate generating functions and bivariate Laplace transforms are the basic tools used in generalizing the standard theory of univariate renewal processes. An example involving a bivariate exponential distribution is presented. This is used to illustrate the general theory and explicit expressions for the two-dimensional renewal density, the two-dimensional renewal function, the correlation between the marginal univariate renewal counting processes, and other related quantities are derived.

Keywords

TWO-DIMENSIONAL RENEWAL THEORYBIVARIATE GENERATING FUNCTIONSBIVARIATE LAPLACE TRANSFORMSRENEWAL FUNCTIONSRENEWAL DENSITIESBIVARIATE EXPONENTIAL DISTRIBUTION
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 2 , June 1974 , pp. 376 - 391
Copyright
Copyright © Applied Probability Trust 1974 

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References

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