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

This article is cited in 9 scientific papers (total in 9 papers)

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

Full text: PDF file (500 kB)
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English version:
Discrete Mathematics and Applications, 2016, 26:2, 71–88

Bibliographic databases:

Document Type: Article
UDC: 519.218.23
Received: 28.04.2015

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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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. V. I. Afanasyev, “On a decomposable branching process with two types of particles”, Proc. Steklov Inst. Math., 294 (2016), 1–12  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. Elena E. D'yakonova, “Reduced multitype critical branching processes in random environment”, Discrete Math. Appl., 28:1 (2018), 7–22  mathnet  crossref  crossref  mathscinet  isi  elib
    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  mathnet  crossref  crossref  mathscinet  isi  elib
    5. G. K. Kobanenko, “Predelnye teoremy dlya ogranichennykh vetvyaschikhsya protsessov”, Diskret. matem., 29:2 (2017), 18–28  mathnet  crossref  elib
    6. V. A. Vatutin, E. E. D'yakonova, “Decomposable branching processes with two types of particles”, Discrete Math. Appl., 28:2 (2018), 119–130  mathnet  crossref  crossref  isi  elib
    7. E. E. D'yakonova, “A subcritical decomposable branching process in a mixed environment”, Discrete Math. Appl., 28:5 (2018), 275–283  mathnet  crossref  crossref  isi  elib
    8. V. I. Afanasyev, “A Functional Limit Theorem for Decomposable Branching Processes with Two Particle Types”, Math. Notes, 103:3 (2018), 337–347  mathnet  crossref  crossref  isi  elib
    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  mathnet  crossref
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