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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

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Volume 28, Issue 2

Issues

Decomposable branching processes with two types of particles

Vladimir A. Vatutin / Elena E. Dyakonova
Published Online: 2018-04-09 | DOI: https://doi.org/10.1515/dma-2018-0012

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 Ξ2, the total number of the second type particles ever born in the process is found. Limit theorems are proved describing (as N → ∞) the conditional distribution of the amount of the first type particles in different generations given that either Ξ2 = N or Ξ2 > N.

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

Originally published in Diskretnaya Matematika (2018) 30,№1, 3–18 (in Russian).

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About the article

Received: 2017-10-20

Published Online: 2018-04-09

Published in Print: 2018-04-25


Funding Source: Russian Science Foundation

Award identifier / Grant number: 14-50-00005

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


Citation Information: Discrete Mathematics and Applications, Volume 28, Issue 2, Pages 119–130, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265, DOI: https://doi.org/10.1515/dma-2018-0012.

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