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 Diskr. Mat., 2015, Volume 27, Issue 2, Pages 22–44 (Mi dm1323)

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

V. I. Afanasyev

Steklov Mathematical Institute of RAS

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. \def\acknowledgementname{Funding

Keywords: decomposable Galton – Watson process with several types of particles, functional limit theorems.

 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/dm1323

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English version:
Discrete Mathematics and Applications, 2016, 26:2, 71–88

Bibliographic databases:

Document Type: Article
UDC: 519.218.23

Citation: V. I. Afanasyev, “Functional limit theorems for the decomposable branching process with two types of particles”, Diskr. Mat., 27:2 (2015), 22–44; Discrete Math. Appl., 26:2 (2016), 71–88

Citation in format AMSBIB
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• https://doi.org/10.4213/dm1323
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This publication is cited in the following articles:
1. Vladimir A. Vatutin, Elena E. Dyakonova, “Extinction of decomposable branching processes”, Discrete Math. Appl., 26:3 (2016), 183–192
2. V. I. Afanasyev, “On a decomposable branching process with two types of particles”, Proc. Steklov Inst. Math., 294 (2016), 1–12
3. Elena E. D'yakonova, “Reduced multitype critical branching processes in random environment”, Discrete Math. Appl., 28:1 (2018), 7–22
4. V. A. Vatutin, “A Conditional Functional Limit Theorem for Decomposable Branching Processes with Two Types of Particles”, Math. Notes, 101:5 (2017), 778–789
5. G. K. Kobanenko, “Predelnye teoremy dlya ogranichennykh vetvyaschikhsya protsessov”, Diskret. matem., 29:2 (2017), 18–28
6. V. A. Vatutin, E. E. D'yakonova, “Decomposable branching processes with two types of particles”, Discrete Math. Appl., 28:2 (2018), 119–130
7. E. E. D'yakonova, “A subcritical decomposable branching process in a mixed environment”, Discrete Math. Appl., 28:5 (2018), 275–283
8. V. I. Afanasyev, “A Functional Limit Theorem for Decomposable Branching Processes with Two Particle Types”, Math. Notes, 103:3 (2018), 337–347
9. V. A. Vatutin, “Uslovnaya predelnaya teorema dlya blizkikh k kriticheskim vetvyaschikhsya protsessov s finalnym tipom chastits”, Matem. vopr. kriptogr., 9:4 (2018), 53–72
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