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Diskr. Mat., 2015, Volume 27, Issue 4, Pages 26–37 (Mi dm1345)  

This article is cited in 8 scientific papers (total in 8 papers)

Extinction of decomposable branching processes

Vladimir A. Vatutin, Elena E. Dyakonova

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: The asymptotic behavior, as $n\rightarrow \infty $, of the conditional distribution of the number of particles in a decomposable critical branching process $\mathbf{Z}(m)=(Z_{1}(m),\ldots,Z_{N}(m))$ with $N$ types of particles at moment $m=n-k,  k=o(n)$, is investigated given that the extinction moment of the process equals to $n$.

Keywords: decomposable branching processes, criticality, conditional 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/dm1345

Full text: PDF file (484 kB)
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English version:
Discrete Mathematics and Applications, 2016, 26:3, 183–192

Bibliographic databases:

ArXiv: 1509.00759
UDC: 519.218.24
Received: 18.06.2015

Citation: Vladimir A. Vatutin, Elena E. Dyakonova, “Extinction of decomposable branching processes”, Diskr. Mat., 27:4 (2015), 26–37; Discrete Math. Appl., 26:3 (2016), 183–192

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. 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
    2. 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
    3. 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
    4. G. K. Kobanenko, “Predelnye teoremy dlya ogranichennykh vetvyaschikhsya protsessov”, Diskret. matem., 29:2 (2017), 18–28  mathnet  crossref  elib
    5. 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
    6. 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
    7. 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
    8. 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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