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Mat. Zametki, 2005, Volume 77, Issue 4, Pages 544–550 (Mi mz2516)  

This article is cited in 4 scientific papers (total in 4 papers)

General scheme of maxima of sums of independent random variables and its applications

A. V. Lebedev

M. V. Lomonosov Moscow State University

Abstract: A general scheme of maxima of sums of independent random variables is introduced. We prove a theorem on the convergence of the maxima in probability. We study its applications to large jumps in random walks and to extrema of shot-noise fields in the case of regularly varying tails. Nondegenerate limiting laws are obtained.

DOI: https://doi.org/10.4213/mzm2516

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English version:
Mathematical Notes, 2005, 77:4, 503–509

Bibliographic databases:

UDC: 519.214.4
Received: 05.05.2003
Revised: 21.06.2004

Citation: A. V. Lebedev, “General scheme of maxima of sums of independent random variables and its applications”, Mat. Zametki, 77:4 (2005), 544–550; Math. Notes, 77:4 (2005), 503–509

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Lebedev, “Activity Maxima in Random Networks in the Heavy Tail Case”, Problems Inform. Transmission, 44:2 (2008), 156–160  mathnet  crossref  mathscinet  isi
    2. A. V. Lebedev, “Maksimumy aktivnosti v bezmasshtabnykh sluchainykh setyakh s tyazhelymi khvostami”, Inform. i ee primen., 5:4 (2011), 25–28  mathnet
    3. A. V. Lebedev, “Activity maxima in some models of information networks with random weights and heavy tails”, Problems Inform. Transmission, 51:1 (2015), 66–74  mathnet  crossref  isi  elib
    4. A. V. Lebedev, “Ekstremalnye indeksy v skheme serii i ikh prilozheniya”, Inform. i ee primen., 9:3 (2015), 39–54  mathnet  crossref  elib
  • Математические заметки Mathematical Notes
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