Renewal theory in two dimensions: bounds on the renewal function

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1977 English Publisher:Cambridge University Press (CUP)Journal:Advances in Applied Probability, volume 9, pages 527-541 (issn: 0001-8678, eissn: 1475-6064,

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Authors: Hunter, Jeffrey J.;

doi: 10.2307/1426112

Renewal theory in two dimensions: bounds on the renewal function

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Abstract

In two earlier papers [6], [7] the properties of bivariate renewal processes and their associated two-dimensional renewal functions, H( x , y ) were examined. By utilising the Fréchet bounds for joint distributions and the properties of univariate renewal processes, a collection of upper and lower bounds for H( x , y ) are constructed. The evaluation of these bounds is carried out for the case of the family of bivariate Poisson processes. An interesting by-product of this investigation leads to a new inequality for the median of a Poisson random variable.

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University of Auckland
New Zealand

Keywords

Renewal theory

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