Geodesic
Reduced critical Bellman--Harris branching processes for small populations
Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 25-39

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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.
Keywords: Bellman-Harris branching process, reduced process, conditional limit theorem. 
@article{DM_2018_30_3_a2,
     author = {V. A. Vatutin and W. Hong and Ya. Ji},
     title = {Reduced critical {Bellman--Harris} branching processes for small populations},
     journal = {Diskretnaya Matematika},
     pages = {25--39},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_3_a2/}
}
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V. A. Vatutin; W. Hong; Ya. Ji. Reduced critical Bellman--Harris branching processes for small populations. Diskretnaya Matematika, Tome 30 (2018) no. 3, pp. 25-39. http://geodesic.mathdoc.fr/item/DM_2018_30_3_a2/