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Tr. Mat. Inst. Steklova, 2015, Volume 290, Pages 114–135 (Mi tm3632)  

This article is cited in 11 scientific papers (total in 11 papers)

Decomposable branching processes with a fixed extinction moment

V. A. Vatutin, E. E. D'yakonova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: The asymptotic behavior as $n\to \infty $ of the probability of the event that a decomposable critical branching process $\mathbf Z(m)= (Z_1(m),…,Z_N(m))$, $m=0,1,2,…$, with $N$ types of particles dies at moment $n$ is investigated, and conditional limit theorems are proved that describe the distribution of the number of particles in the process $\mathbf Z(\cdot )$ at moment $m<n$ given that the extinction moment of the process is $n$. These limit theorems can be considered as statements describing the distribution of the number of vertices in the layers of certain classes of simply generated random trees of fixed height.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968515030103

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 290:1, 103–124

Bibliographic databases:

Document Type: Article
UDC: 519.218.24
Received: March 15, 2015

Citation: V. A. Vatutin, E. E. D'yakonova, “Decomposable branching processes with a fixed extinction moment”, Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Tr. Mat. Inst. Steklova, 290, MAIK Nauka/Interperiodica, Moscow, 2015, 114–135; Proc. Steklov Inst. Math., 290:1 (2015), 103–124

Citation in format AMSBIB
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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. C. Smadi, V. A. Vatutin, “Reduced two-type decomposable critical branching processes with possibly infinite variance”, Markov Process. Relat. Fields, 22:2 (2016), 311–358  mathscinet  zmath  isi
    5. 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
    6. G. K. Kobanenko, “Predelnye teoremy dlya ogranichennykh vetvyaschikhsya protsessov”, Diskret. matem., 29:2 (2017), 18–28  mathnet  crossref  elib
    7. 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
    8. 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
    9. 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
    10. M. Liu, V. A. Vatutin, “Reduced critical branching processes for small populations”, Theory Probab. Appl., 63:4 (2019), 648–656  mathnet  crossref  crossref  isi  elib
    11. 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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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