On rare and extreme events
type: Item
instance of: scholarly article
title: On rare and extreme events
zbMATH Open document ID: 1019.60044
DOI: 10.1016/S0960-0779(00)00046-1
author: Henri-François Raynaud
author: Thierry E. Huillet
published in: Chaos, Solitons and Fractals
publication date: 2003-03-19T00:00:00Z
review text: Let \(0< S_1< S_2< \dots\) form a point process. Let \(X_1,X_2,\dots\) be independent and identically distributed random variables with common distribution function \(F(x)\). The authors review limit theorems available for the sum of \(X_{S_j}\), \(S_j\leq T\), \(T\to+\infty\), under a variety of assumptions on the point process \(S_j\), \(j\geq 1\), and on \(1- F(x)\) as \(x\to+\infty\). The results are then interpreted in terms of practical applications.
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 1884588
zbMATH Keywords: renewal process
zbMATH Keywords: Pareto tail
zbMATH Keywords: infinite variance
zbMATH Keywords: infinite expectation
zbMATH Keywords: partial sums
zbMATH Keywords: limit theorems
reviewed by: Janos Galambos
MaRDI profile type: Publication
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full work available at URL: s0960-0779(00)00046-1
OpenAlex ID: W2042989654
description: scientific article; zbMATH DE number 1884588