A contribution to large deviations for heavy-tailed random sums
type: Item
instance of: scholarly article
title: A contribution to large deviations for heavy-tailed random sums
zbMATH Open document ID: 1015.60025
DOI: 10.1007/BF02881880
author: Chun Su
author: Tao Jiang
author: Qihe Tang
published in: Science in China. Series A
publication date: 2002-08-15T00:00:00Z
review text: Let \(\{X_n:n\geq 1\}\) be a sequence of independent and nonnegative random variables with a common distribution function \(F(x)\) and \(\{N(t): t\geq 0\}\) a process of nonnegative, integer-valued random variables independent of \(\{X_n: n\geq 1\}\). \textit{C. Klüppelberg} and \textit{T. Mikosch} [J. Appl. Probab. 34, No. 2, 293-308 (1997; Zbl 0903.60021)] proved a theorem of large deviation for the random sum of \(X_n\) from 1 to \(N(t)\) when \(F(x)\) belongs to a so-called extended regular variation class and under some conditions on the convergence rate of \(N(t)\) as \(t\) tends to infinity, one of them was claimed by the authors of this paper as too strict and not even satisfied by the common renewal processes. The same result under a much weaker condition is proved in this paper and applied to a renewal risk model in insurance and finance.
reviewed by: Dongsheng Tu
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60K10
zbMATH DE Number: 1782100
zbMATH Keywords: large deviations
zbMATH Keywords: random sum
zbMATH Keywords: heavy-tailed distribution
zbMATH Keywords: risk model in insurance and finance
zbMATH Keywords: renewal processes
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02881880
OpenAlex ID: W2010935363
description: scientific article; zbMATH DE number 1782100