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A Central Limit Theorem for Cumulative 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; E95/B673, IBM Corporation, P.O. Box 12195, Research Triangle Park, NC 27709, USA.
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Abstract

A central limit theorem for cumulative processes was first derived by Smith (1955). No remainder term was given. We use a different approach to obtain such a term here. The rate of convergence is the same as that in the central limit theorems for sequences of independent random variables.

Keywords

RATE OF CONVERSIONRENEWAL PROCESS

MSC classification

Primary: 60K05: Renewal theory
Secondary: 60F05: Central limit and other weak theorems
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 1 , March 1994 , pp. 104 - 121
Copyright
Copyright © Applied Probability Trust 1994 

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