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A simple coupling of renewal processes

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

T. Lindvall
T. Lindvall*
Affiliation:
University of Göteborg
*
∗Postal address: Department of Mathematics, University of Göteborg, S-41296 Göteborg, Sweden.
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Abstract

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We use a simple coupling to prove the classical result that the renewal function U of a zero-delayed renewal process satisfies U(t) – λ . t→λ2μ2/2 as t→∞ if the life-length distribution is of non-lattice type and has finite first and second moments μ and μ2 respectively; λ is the renewal intensity, and is equal to 1/μ.

Keywords

COUPLINGRENEWAL FUNCTION

MSC classification

Primary: 60K05: Renewal theory
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 24 , Issue 4 , December 1992 , pp. 1010 - 1011
Copyright
Copyright © Applied Probability Trust 1992 

References

Feller, W. (1966) An Introduction to Probability Theory and its Applications , Vol. II. Wiley, New York.Google Scholar
Lindvall, T. (1992) Lectures on the Coupling Method . Wiley, New York.Google Scholar