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# Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

6 Issues per year

CiteScore 2016: 0.16

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.552

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1569-3929
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Volume 26, Issue 2

# Functional limit theorems for the decomposable branching process with two types of particles

Valeriy I Afanasiev
Published Online: 2016-04-26 | DOI: https://doi.org/10.1515/dma-2016-0006

## Abstract

A decomposable Galton - Watson process with two types of particles is considered. Particles of the first type produce equal random numbers of particles of both types, particles of the second type produce particles of the second type only. Under the condition that the total number of the first type particles is equal to N the functional limit theorems are proved for the numbers of particles of both types existing at times of the orders of $\sqrt{N}$, of N and of the intermediate orders.

Originally published in Diskretnaya Matematika (2015) 27, N2, 22-44 (in Russian).

## References

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Kolchin V.F., “Random mappings”, Trans. Ser. in Math. and Eng., Optimization Software Inc. Publications Division, New York, 1986, 207 pp.Google Scholar

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Drmota M., “On the profile of random trees”, Random Struct. Alg., 10 :4 (1997), 421-451.Google Scholar

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Lamperti J., “Limiting distributions for branching processes”, Univ. California Press., Proc. Fifth Berkeley Sympos. Math. Statist. and Probab., 1967, 225-241.Google Scholar

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Lindvall T., “Convergence of critical Galton-Watson branching processes”, J. Appl. Probab., 9 :2 (1972), 445-450.Google Scholar

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Billingsley P., Convergence of probability measures, Wiley, 1968, 262 pp.Google Scholar

Published Online: 2016-04-26

Published in Print: 2016-04-01

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 26, Issue 2, Pages 71–88, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265,

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© 2016 Walter de Gruyter GmbH, Berlin/Boston.

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