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A central limit theorem by remainder term for renewal processes

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  01 July 2016

Allen L. Roginsky
Allen L. Roginsky*
Affiliation:
IBM Corporation
*
∗ Postal address: IBM Corporation, P.O. Box 12195, Research Triangle Park, NC 27709, USA.
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Abstract

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

Keywords

RATES OF CONVERGENCE

MSC classification

Primary: 60K05: Renewal theory
Secondary: 60F05: Central limit and other weak theorems
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 2 , June 1992 , pp. 267 - 287
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

This research was conducted while the author was a graduate student at the Department of Statistics, University of North Carolina at Chapel Hill

References

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