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Renewal theory in two dimensions: asymptotic 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 an earlier paper (Renewal theory in two dimensions: Basic results) the author developed a unified theory for the study of bivariate renewal processes. In contrast to this aforementioned work where explicit expressions were obtained, we develop some asymptotic results concerning the joint distribution of the bivariate renewal counting process (Nx(1), Ny(2)), the distribution of the two-dimensional renewal counting process Nx,y and the two-dimensional renewal function &Nx,y. A by-product of the investigation is the study of the distribution and moments of the minimum of two correlated normal random variables. A comprehensive bibliography on multi-dimensional renewal theory is also appended.

Keywords

TWO-DIMENSIONAL RENEWAL THEORYRENEWAL FUNCTIONSASYMPTOTIC DISTRIBUTIONSMINIMUM OF TWO CORRELATED NORMAL RANDOM VARIABLES
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 3 , September 1974 , pp. 546 - 562
Copyright
Copyright © Applied Probability Trust 1974 

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References

Bibliography on multi-dimensional renewal theory

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Additional references

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