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 Inform. Primen., 2015, Volume 9, Issue 3, Pages 39–54 (Mi ia379)

Extremal indices in a series scheme and their applications

A. V. Lebedev

Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation

Abstract: The concept of an extremal index of a stationary random sequence is generalized to a series scheme of identically distributed random variables with random series sizes tending to infinity in probability. The new extremal indices are introduced through two definitions generalizing the basic properties of the classical extremal index. Some useful properties of the new extremal indices are proved. The paper shows how the behavior of aggregate activity maxima on random graphs (in information network models) and the behavior of maxima of random particles scores in branching processes (in biological populations models) can be described in terms of the new extremal indices. New results on models with copulas and threshold models are obtained. The paper shows that the new indices can take different values for one system and the values greater than one.

Keywords: extremal index; series scheme; random graph; information network; branching process; copula.

DOI: https://doi.org/10.14357/19922264150305

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Citation: A. V. Lebedev, “Extremal indices in a series scheme and their applications”, Inform. Primen., 9:3 (2015), 39–54

Citation in format AMSBIB
\Bibitem{Leb15} \by A.~V.~Lebedev \paper Extremal indices in a series scheme and their applications \jour Inform. Primen. \yr 2015 \vol 9 \issue 3 \pages 39--54 \mathnet{http://mi.mathnet.ru/ia379} \crossref{https://doi.org/10.14357/19922264150305} \elib{https://elibrary.ru/item.asp?id=24223471} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. A. Goldaeva, A. V. Lebedev, “On extremal indices greater than one for a scheme of series”, Lith. Math. J., 58:4 (2018), 384–398
2. A. V. Lebedev, “Multivariate Extremes of Random Scores of Particles in Branching Processes with Max-Linear Inheritance”, Math. Notes, 105:3 (2019), 376–384
3. N. M. Markovich, I. V. Rodionov, “Maxima and sums of non-stationary random length sequences”, Extremes, 23:3 (2020), 451–464
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