Local limit theorems for shock models

Edward Omey () and Rein Vesilo ()
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Edward Omey: Hogeschool-Universiteit Brussel (HUB), Belgium
Rein Vesilo: Macquarie University, Dept. of Electronics, Sydney, Australia

No 2011/23, Working Papers from Hogeschool-Universiteit Brussel, Faculteit Economie en Management

Abstract: In this paper we study the local behaviour of a characteristic of two types of shock models. In many physical systems, a failure occurs when the stress or the fatigue, represented by $\epsilon(n)$, reaches a critical level $x$. We are interested in the time $\tau(x)$ for which this happens for the first time. In the cumulative shock model we assume that $\epsilon(n) = \sum_{i=1}^n X_i$ is an acummulation of independent shocks $\Ksi_i$. In the extreme shock model, we assume that $\epsilon(n) = \max(X_1,X_2, ..., X_n)$ where the damage to the system is measured in terms of the largest shock up to now. For both models we.obtain a local limit theorem for the corresponding time $\tau(x)$.

Keywords: Renewal theory; shock models; regular variation; extreme value theory; local limit theory (search for similar items in EconPapers)
Pages: 26 page
Date: 2011-09
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Citations: View citations in EconPapers (1)

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