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Limit theorems for jump shock models

Published online by Cambridge University Press:  14 July 2016

Keigo Yamada
Keigo Yamada*
Affiliation:
University of Tsukuba
*
∗ Postal address: Institute of Information Sciences and Electronics, University of Tsukuba, Ibaraki 305, Japan.
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Abstract

We consider an additive shock process where shocks occur according to a Poisson point process and they are accumulated in an appropriate way to the damage. It is shown that suitably normalized shock processes converge weakly to a process which is represented as a sum of a stable process and a deterministic process.

Keywords

STABLE PROCESSPOISSON POINT PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 793 - 806
Copyright
Copyright © Applied Probability Trust 1989 

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