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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2013 Volume 412, Pages 207–214 (Mi znsl5650)

This article is cited in 1 paper

Cyclic behavior of the maximum of sums of independent random variables

M. A. Lifshitsab

a St. Petersburg State University, St. Petersburg, Russia
b MAI, Linköping University, Linköping, Sweden

Abstract: In a recent author's work the cyclic behavior of maxima in a hierarchical summation scheme was discovered. In the present note we show how the same phenomenon appears in the scheme of conventional summation: the distribution of maximum of $2^n$ independent copies of a sum of $n$ i.i.d. random variables approaches, as $n$ grows, some helix in the space of distributions.

Key words and phrases: distribution of maximum, sums of independent random variables, large deviations, cyclic limit theorem.

UDC: 519.21

Received: 02.12.2012


 English version:
Journal of Mathematical Sciences (New York), 2015, 204:1, 134–139

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