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Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 4, Pages 791–794 (Mi tvp196)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Maxima of independent sums in the presence of heavy tails

A. V. Lebedev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Let
$$Y_{mn}=\max_{1\le i\le m}\sum_{j=1}^n X_{ij},\qquad m,n\ge 1,$$
be a family of extremes, where $X_{ij}$, $i,j\ge 1$, are independent with common subexponential distribution $F$. The limit behavior of $Y_{mn}$ is investigated as $m,n\to\infty$. Various nondegenerate limit laws are obtained (Fréchet and Gumbel), depending on the relative rate of growth of $m,n$ and the tail behavior of $F$.

Keywords: maxima, sums, regularly varying tails, subexponentiality, nondegenerate limit laws, linear scaling

DOI: https://doi.org/10.4213/tvp196

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English version:
Theory of Probability and its Applications, 2005, 49:4, 700–703

Bibliographic databases:

Received: 17.03.2003

Citation: A. V. Lebedev, “Maxima of independent sums in the presence of heavy tails”, Teor. Veroyatnost. i Primenen., 49:4 (2004), 791–794; Theory Probab. Appl., 49:4 (2005), 700–703

Citation in format AMSBIB
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    Erratum

    This publication is cited in the following articles:
    1. T. V. Kuznetsova, “Limit theorems for maxima of some dependent random sums”, Moscow University Mathematics Bulletin, 67:3 (2012), 107–111  mathnet  crossref  mathscinet
  •     Theory of Probability and its Applications
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