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Diskr. Mat., 2016, Volume 28, Issue 4, Pages 58–79 (Mi dm1393)  

This article is cited in 2 scientific papers (total in 2 papers)

Reduced multitype critical branching processes in random environment

Elena E. D'yakonova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We consider a multitype critical branching process $\mathbf{Z}_{n},n=0,1,...$, in an i.i.d. random environment. Let $Z_{m,n}$ be the number of particles in this process at time $m$ having descendants at time $n$. A limit theorem is proved for the logarithm of $Z_{nt,n}$ at moments $nt, 0\leq t\leq 1,$ conditioned on the survival of the process $\mathbf{Z}_{n}$ up to moment $n$ when $n\rightarrow \infty $.

Keywords: multitupe branching processes, reduced branching processes, random environment.

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/dm1393

Full text: PDF file (578 kB)
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English version:
Discrete Mathematics and Applications, 2018, 28:1, 7–22

Bibliographic databases:

UDC: 519.218.27
Received: 25.10.2016

Citation: Elena E. D'yakonova, “Reduced multitype critical branching processes in random environment”, Diskr. Mat., 28:4 (2016), 58–79; Discrete Math. Appl., 28:1 (2018), 7–22

Citation in format AMSBIB
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\paper Reduced multitype critical branching processes in random environment
\jour Diskr. Mat.
\yr 2016
\vol 28
\issue 4
\pages 58--79
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\jour Discrete Math. Appl.
\yr 2018
\vol 28
\issue 1
\pages 7--22
\crossref{https://doi.org/10.1515/dma-2018-0002}
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  • http://mi.mathnet.ru/eng/dm/v28/i4/p58

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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, “Multitype branching processes in random environment: survival probability for the critical case”, Theory Probab. Appl., 62:4 (2018), 506–521  mathnet  crossref  crossref  zmath  isi  elib
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