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Weak convergence of an iterated renewal process

Published online by Cambridge University Press:  14 July 2016

Pranab Kumar Sen
Pranab Kumar Sen*
Affiliation:
University of North Carolina
*
∗Postal address: Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27514, U.S.A.
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Abstract

Asymptotic normality and the weak invariance principle are studied for an iterated renewal process of order A martingale decomposition is used in this context to provide a simple proof.

Keywords

ASYMPTOTIC NORMALITYMARTINGALERENEWAL PROCESSWEAK CONVERGENCETIGHTNESSWIENER PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 291 - 296
Copyright
Copyright © Applied Probability Trust 

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Footnotes

Research partially supported by the National Institutes of Health, Contract No. NIH-NHLBI–71–2243–L from the National Heart, Lung and Blood Institute.

References

Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Brown, B. M. (1971) Martingale central limit theorems. Ann. Math. Statist. 42, 59–66.Google Scholar
Hájek, J. and Židák, Z. (1967) Theory of Rank Tests. Academic Press, New York.Google Scholar