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Cumulative shock models

Published online by Cambridge University Press:  01 July 2016

Allan Gut
Allan Gut*
Affiliation:
Uppsala University
*
∗Postal address: Uppsala University, Department of Mathematics, Thunbergsvägen 3, S-752 38 Uppsala, Sweden.
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Abstract

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We show that a theory for stopped two-dimensional random walks is well suited to describe cumulative shock models. Limit theorems for the lifetime/failure time of a system are provided.

Keywords

SHOCKINTERSHOCK TIMESTOPPED RANDOM WALKRENEWAL THEORYFIRST-PASSAGE TIMESSTRONG LAWCENTRAL LIMIT THEOREMLAW OF THE ITERATED LOGARITHMMOMENT CONVERGENCEINSURANCE RISK THEORY
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 504 - 507
Copyright
Copyright © Applied Probability Trust 1990 

References

Anderson, K. K. (1988) A note on cumulative shock models. J. Appl. Prob. 25, 220–223.CrossRefGoogle Scholar
Gut, A. (1988) Stopped Random Walks. Limit Theorems and Applications. Springer-Verlag, New York.CrossRefGoogle Scholar
Gut, A. and Janson, S. (1983) The limiting behaviour of certain stopped sums and some applications. Scand. J. Statist. 10, 281–292.Google Scholar
Sumita, U. and Shanthikumar, J. G. (1985) A class of correlated cumulative shock models. Adv. Appl. Prob. 17, 347–366.Google Scholar