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Mat. Zametki, 2018, Volume 103, Issue 3, Pages 323–335 (Mi mz11601)  

This article is cited in 3 scientific papers (total in 3 papers)

A Functional Limit Theorem for Decomposable Branching Processes with Two Particle Types

V. I. Afanasyev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A decomposable Galton–Watson branching process with two particle types is studied. It is assumed that the particles of the first type produce equal numbers of particles of the first and second types, while the particles of the second type produce only particles of their own type. Under the condition that the total number of particles of the second type is greater than $N\to \infty$, a functional limit theorem for the process describing the number of particles of the first type in different generations is proved.

Keywords: decomposable Galton–Watson branching process, local time of a Brownian excursion, functional limit theorems.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/mzm11601

Full text: PDF file (495 kB)
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English version:
Mathematical Notes, 2018, 103:3, 337–347

Bibliographic databases:

UDC: 519.218
Received: 24.03.2017
Revised: 05.06.2017

Citation: V. I. Afanasyev, “A Functional Limit Theorem for Decomposable Branching Processes with Two Particle Types”, Mat. Zametki, 103:3 (2018), 323–335; Math. Notes, 103:3 (2018), 337–347

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/mz/v103/i3/p323

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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. V. A. Vatutin, E. E. D'yakonova, “Decomposable branching processes with two types of particles”, Discrete Math. Appl., 28:2 (2018), 119–130  mathnet  crossref  crossref  isi  elib
    2. E. E. D'yakonova, “A subcritical decomposable branching process in a mixed environment”, Discrete Math. Appl., 28:5 (2018), 275–283  mathnet  crossref  crossref  isi  elib
    3. V. A. Vatutin, “Uslovnaya predelnaya teorema dlya blizkikh k kriticheskim vetvyaschikhsya protsessov s finalnym tipom chastits”, Matem. vopr. kriptogr., 9:4 (2018), 53–72  mathnet  crossref
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