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Diskr. Mat., 2018, Volume 30, Issue 2, Pages 14–26 (Mi dm1501)  

A subcritical decomposable branching process in a mixed environment

E. E. D'yakonova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A two-type decomposable branching process 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. The reproduction law of the first type particles is specified by a random environment. The reproduction law of the second type particles is one and the same for all generations. A limit theorem is proved describing the conditional distribution of the number of particles in the process at time $nt,t\in (0,1]$, given the survival of the process up to moment $n\rightarrow \infty .$

Keywords: branching process, mixed environment, limit theorem

Funding Agency Grant Number
Russian Science Foundation 14-50-00005


DOI: https://doi.org/10.4213/dm1501

Full text: PDF file (442 kB)
First page: PDF file
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English version:
Discrete Mathematics and Applications, 2018, 28:5, 275–283

Bibliographic databases:

Document Type: Article
UDC: 519.218.27
Received: 05.02.2018
Revised: 14.05.2018

Citation: E. E. D'yakonova, “A subcritical decomposable branching process in a mixed environment”, Diskr. Mat., 30:2 (2018), 14–26; Discrete Math. Appl., 28:5 (2018), 275–283

Citation in format AMSBIB
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  • https://doi.org/10.4213/dm1501
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