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Matematicheskie Zametki, 2005, Volume 77, Issue 4, Pages 544–550
DOI: https://doi.org/10.4213/mzm2516 (Mi mzm2516) 		 
This article is cited in 5 scientific papers (total in 5 papers)

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

A. V. Lebedev

M. V. Lomonosov Moscow State University
Full-text PDF (199 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm2516
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.
Received: 05.05.2003
Revised: 21.06.2004
English version:
Mathematical Notes, 2005, Volume 77, Issue 4, Pages 503–509
DOI: https://doi.org/10.1007/s11006-005-0050-y
Bibliographic databases:
UDC: 519.214.4
Language: Russian
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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Linking options:
  • https://www.mathnet.ru/eng/mzm2516
  • https://doi.org/10.4213/mzm2516
  • https://www.mathnet.ru/eng/mzm/v77/i4/p544
    • This publication is cited in the following 5 articles:
    1. Alexey Los, Aleksandr Belov, 2021 XVII International Symposium “Problems of Redundancy in Information and Control Systems” (REDUNDANCY), 2021, 80  crossref
    2. 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
    3. A. V. Lebedev, “Ekstremalnye indeksy v skheme serii i ikh prilozheniya”, Inform. i ee primen., 9:3 (2015), 39–54  mathnet  crossref  elib
    4. A. V. Lebedev, “Maksimumy aktivnosti v bezmasshtabnykh sluchainykh setyakh s tyazhelymi khvostami”, Inform. i ee primen., 5:4 (2011), 25–28  mathnet
    5. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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