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Tr. Mat. Inst. Steklova, 2016, Volume 294, Pages 7–19 (Mi tm3724)  

This article is cited in 6 scientific papers (total in 6 papers)

On a decomposable branching process with two types of particles

V. I. Afanasyev

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: A decomposable Galton–Watson branching process with two types of particles is considered. It is assumed that particles of the first type produce particles of both the first and the second types, and produce them in equal amounts, while particles of the second type only produce particles of the same type. An asymptotic formula is obtained for the probability that the total number of particles of the second type up to time $N$ is greater than $\theta N$, where $\theta$ is a positive constant and $N\to\infty$. A limit theorem is established for the total number of particles of the first type considered under the condition that the total number of particles of the second type up to time $N$ is greater than $\theta N$.

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


DOI: https://doi.org/10.1134/S0371968516030018

Full text: PDF file (188 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 294, 1–12

Bibliographic databases:

Document Type: Article
UDC: 519.218.23
Received: April 20, 2016

Citation: V. I. Afanasyev, “On a decomposable branching process with two types of particles”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Tr. Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 7–19; Proc. Steklov Inst. Math., 294 (2016), 1–12

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    This publication is cited in the following articles:
    1. V. A. Vatutin, “A Conditional Functional Limit Theorem for Decomposable Branching Processes with Two Types of Particles”, Math. Notes, 101:5 (2017), 778–789  mathnet  crossref  crossref  mathscinet  isi  elib
    2. G. K. Kobanenko, “Predelnye teoremy dlya ogranichennykh vetvyaschikhsya protsessov”, Diskret. matem., 29:2 (2017), 18–28  mathnet  crossref  elib
    3. 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
    4. 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
    5. V. I. Afanasyev, “A Functional Limit Theorem for Decomposable Branching Processes with Two Particle Types”, Math. Notes, 103:3 (2018), 337–347  mathnet  crossref  crossref  isi  elib
    6. 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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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