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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, Number 3, Pages 18–23 (Mi vmumm491)  

Mathematics

Limit theorems for maxima of some dependent random sums

T. V. Kuznetsova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A family of extrema having form
$$ Y_{mn}=\max_{1\le i \le m}\sum_{j=1}^n X_{ij},\qquad m,n\ge1, $$
is considered, here the random variables $\{X_{ij}\}$, $i\ge1$, $j\ge1$, are dependent by columns (with identical $j$) and independent by rows (with different $j$). The asymptotics of $Y_{mn}$ for $m,n\to\infty$ is studied. Three particular cases are considered: a normal distribution, a Laplace distribution, and an $\alpha$-stable distribution.

Key words: maxima, random sums, $\alpha$-stable distribution, Frechet distribution.

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English version:
Moscow University Mathematics Bulletin, 2012, 67:3, 107–111

Bibliographic databases:

UDC: 519.2
Received: 30.03.2011

Citation: T. V. Kuznetsova, “Limit theorems for maxima of some dependent random sums”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 3, 18–23; Moscow University Mathematics Bulletin, 67:3 (2012), 107–111

Citation in format AMSBIB
\Bibitem{Kuz12}
\by T.~V.~Kuznetsova
\paper Limit theorems for maxima of some dependent random sums
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2012
\issue 3
\pages 18--23
\mathnet{http://mi.mathnet.ru/vmumm491}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3026840}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2012
\vol 67
\issue 3
\pages 107--111
\crossref{https://doi.org/10.3103/S0027132212030047}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864805131}


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