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

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

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 294, 1–12

Bibliographic databases:

UDC: 519.218.23

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

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3724
• https://doi.org/10.1134/S0371968516030018
• http://mi.mathnet.ru/eng/tm/v294/p7

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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
2. G. K. Kobanenko, “Predelnye teoremy dlya ogranichennykh vetvyaschikhsya protsessov”, Diskret. matem., 29:2 (2017), 18–28
3. V. A. Vatutin, E. E. D'yakonova, “Decomposable branching processes with two types of particles”, Discrete Math. Appl., 28:2 (2018), 119–130
4. E. E. D'yakonova, “A subcritical decomposable branching process in a mixed environment”, Discrete Math. Appl., 28:5 (2018), 275–283
5. V. I. Afanasyev, “A Functional Limit Theorem for Decomposable Branching Processes with Two Particle Types”, Math. Notes, 103:3 (2018), 337–347
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
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