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A note on cumulative shock models

Published online by Cambridge University Press:  14 July 2016

Kevin K. Anderson
Kevin K. Anderson*
Affiliation:
IBM Thomas J. Watson Research Center
*
∗ Present address: Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550, USA.
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Abstract

A shock model in which the time intervals between shocks are in the domain of attraction of a stable law of order less than 1 or relatively stable is considered. Weak limit theorems are established for the cumulative magnitude of the shocks and the first time the cumulative magnitude exceeds z without any assumption on the dependence between the intershock interval and shock magnitude.

Keywords

STABLE LAWSREGULAR VARIATIONRANDOM INDICESRENEWAL THEORY

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988, pp. 220 - 223
Copyright
Copyright © Applied Probability Trust 1988 

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References

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