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Diskr. Mat., 2018, Volume 30, Issue 3, Pages 25–39 (Mi dm1532)  

Reduced critical Bellman–Harris branching processes for small populations

V. A. Vatutina, W. Hongb, Ya. Jib

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b School of Mathematical Sciences & Laboratory of Mathematical and Complex Systems, Beijing Normal University

Abstract: A critical Bellman-Harris branching process $\{ Z(t), t\geq 0\} $ with finite variance of the offspring number is considered. Assuming that $0<Z(t)\leq \varphi (t)$, where either $\varphi (t)=o(t)$ as $t\rightarrow \infty $ or $\varphi (t)=at,  a>0$, we study the structure of the process $ \{ Z(s,t),0\leq s\leq t\} ,$ where $Z(s,t)$ is the number of particles in the initial process at moment $s$ which either survive up to moment $t$ or have a positive number of descendants at this moment.

Keywords: Bellman-Harris branching process, reduced process, conditional limit theorem

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
National Natural Science Foundation of China 11531001
11626245


DOI: https://doi.org/10.4213/dm1532

Full text: PDF file (480 kB)
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English version:
Discrete Mathematics and Applications, 2018, 28:5, 319–330

Bibliographic databases:

Document Type: Article
UDC: 519.218.24
Received: 17.05.2018

Citation: V. A. Vatutin, W. Hong, Ya. Ji, “Reduced critical Bellman–Harris branching processes for small populations”, Diskr. Mat., 30:3 (2018), 25–39; Discrete Math. Appl., 28:5 (2018), 319–330

Citation in format AMSBIB
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\pages 319--330
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