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Diskr. Mat., 2018, Volume 30, Issue 1, Pages 3–18 (Mi dm1475)  

This article is cited in 1 scientific paper (total in 1 paper)

Decomposable branching processes with two types of particles

V. A. Vatutin, E. E. D'yakonova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A two-type critical decomposable branching process with discrete time is considered in which particles of the first type may produce at the death moment offspring of both types while particles of the second type may produce at the death moment offspring of their own type only. Assuming that the offspring distributions of particles of both types may have infinite variance, the asymptotic behavior of the tail distribution of the random variable $\Xi _{2},$ the total number of the second type particles ever born in the process is found. Limit theorems are proved describing (as $N\rightarrow \infty $) the conditional distribution of the amount of the first type particles in different generations given that either $\Xi _{2}=N$ or $\Xi _{2}>N.$

Keywords: decomposable branching process, total population size, limit theorem

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant no. 14-50-00005.


DOI: https://doi.org/10.4213/dm1475

Full text: PDF file (518 kB)
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English version:
Discrete Mathematics and Applications, 2018, 28:2, 119–130

Bibliographic databases:

Document Type: Article
UDC: 519.218.27
Received: 20.10.2017

Citation: V. A. Vatutin, E. E. D'yakonova, “Decomposable branching processes with two types of particles”, Diskr. Mat., 30:1 (2018), 3–18; Discrete Math. Appl., 28:2 (2018), 119–130

Citation in format AMSBIB
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\paper Decomposable branching processes with two types of particles
\jour Diskr. Mat.
\yr 2018
\vol 30
\issue 1
\pages 3--18
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\crossref{https://doi.org/10.4213/dm1475}
\elib{http://elibrary.ru/item.asp?id=32641282}
\transl
\jour Discrete Math. Appl.
\yr 2018
\vol 28
\issue 2
\pages 119--130
\crossref{https://doi.org/10.1515/dma-2018-0012}
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  • https://doi.org/10.4213/dm1475
  • http://mi.mathnet.ru/eng/dm/v30/i1/p3

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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. 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
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