Reduced critical Bellman--Harris branching processes for small populations

V. A. Vatutin ; W. Hong ; Ya. Ji

Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 25-39.

Résumé

A critical Bellman-Harris branching process $\left\{ Z(t), t\geq 0\right\} $ with finite variance of the offspring number is considered. Assuming that $0$, 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.

Détail

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

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