This article is cited in 2 papers

Reduced critical Bellman–Harris branching processes for small populations

V. A. Vatutin^a, W. Hong^b, Ya. Ji<sup>b

a</sup> 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 $\left\{ Z(t), t\geq 0\right\} $ 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 $ \left\{ Z(s,t),0\leq s\leq t\right\} ,$ 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.

UDC: 519.218.24

Received: 17.05.2018

DOI: 10.4213/dm1532

 English version: Discrete Mathematics and Applications, 2018, 28:5, 319–330

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