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Matematicheskie Zametki, 2019, Volume 105, Issue 3, Pages 395–405
DOI: https://doi.org/10.4213/mzm11670 (Mi mzm11670) 		 
This article is cited in 6 scientific papers (total in 7 papers)

Multivariate Extremes of Random Scores of Particles in Branching Processes with Max-Linear Inheritance

A. V. Lebedev

Lomonosov Moscow State University
Full-text PDF (548 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm11670
Abstract: The paper continues the author's long-term study of the extrema of random scores of particles in branching processes. It is assumed that the particle scores are dependent via common heredity, the dependence being determined by the distance. The case in which the scores have distributions with heavy tails is considered. The max-linear score generation model is used. The asymptotic behavior of multivariate extremes of scores over generations is studied. Nondegenerate limit laws are obtained for the maxima under linear normalization, and examples are given for various types of branching processes.
Keywords: branching process, multivariate extremum, heavy tail, upper tail dependence coefficient.
Received: 10.05.2017
Revised: 03.04.2018
English version:
Mathematical Notes, 2019, Volume 105, Issue 3, Pages 376–384
DOI: https://doi.org/10.1134/S0001434619030088
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: A. V. Lebedev, “Multivariate Extremes of Random Scores of Particles in Branching Processes with Max-Linear Inheritance”, Mat. Zametki, 105:3 (2019), 395–405; Math. Notes, 105:3 (2019), 376–384
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11670
  • https://www.mathnet.ru/eng/mzm/v105/i3/p395
    Erratum
    This publication is cited in the following 7 articles:
    1. A. V. Lebedev, “Records and increases of multivariate extremes of random particle scores in supercritical branching processes with max-linear heredity”, Theory Probab. Appl., 67:2 (2022), 310–317  mathnet  crossref  crossref  mathscinet  zmath
    2. A. V. Nazmutdinova, “Multidimensional records of particle scores in overcritical branching processes with continuous time”, Moscow University Mathematics Bulletin, 77:6 (2022), 269–276  mathnet  crossref  crossref  mathscinet  zmath  elib
    3. A. V. Lebedev, A. V. Nazmutdinova, “Srednee chislo sovmestnykh skachkov mnogomernykh ekstremumov priznakov chastits v markovskikh vetvyaschikhsya protsessakh. Sluchai kopuly Kleitona”, Sib. elektron. matem. izv., 19:2 (2022), 972–983  mathnet  crossref  mathscinet
    4. Claudia Klüppelberg, Ercan Sönmez, “Max-linear models in random environment”, Journal of Multivariate Analysis, 190 (2022), 104999  crossref  mathscinet
    5. A. V. Karpenko, “Properties of Two-Dimensional Maxima of Particle Scores in Critical Branching Processes with Immigration and Continuous Time”, Math. Notes, 109:2 (2021), 231–240  mathnet  crossref  crossref  mathscinet  isi  elib
    6. A. V. Karpenko, “New properties of bivariate maxima of particle scores in branching processes with continuous time”, Moscow University Mathematics Bulletin, 75:1 (2020), 16–21  mathnet  crossref  mathscinet  zmath  isi
    7. A. V. Lebedev, “Letter to the Editor”, Math. Notes, 107:6 (2020), 1046–1046  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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