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Mat. Zametki, 2017, Volume 101, Issue 5, Pages 669–683 (Mi mz11350)  

This article is cited in 5 scientific papers (total in 5 papers)

A Conditional Functional Limit Theorem for Decomposable Branching Processes with Two Types of Particles

V. A. Vatutin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Consider a critical decomposable branching process with two types of particles in which particles of the first type give birth, at the end of their life, to descendants of the first type, as well as to descendants of the second type, while particles of the second type produce only descendants of the same type at the time of their death. We prove a functional limit theorem describing the distribution for the total number of particles of the second type appearing in the process in time $Nt$, $0\leq t<\infty$, given that the number of particles of the first type appearing in the process during its evolution is $N$.

Keywords: decomposable branching process, total size of the population, functional limit theorem.

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/mzm11350

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English version:
Mathematical Notes, 2017, 101:5, 778–789

Bibliographic databases:

UDC: 519.218
Received: 17.08.2016

Citation: V. A. Vatutin, “A Conditional Functional Limit Theorem for Decomposable Branching Processes with Two Types of Particles”, Mat. Zametki, 101:5 (2017), 669–683; Math. Notes, 101:5 (2017), 778–789

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. G. K. Kobanenko, “Predelnye teoremy dlya ogranichennykh vetvyaschikhsya protsessov”, Diskret. matem., 29:2 (2017), 18–28  mathnet  crossref  elib
    2. 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
    3. 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
    4. 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
    5. 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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