Reduced critical processes for small populations

Minzhi Liu; Vladimir Vatutin

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arXiv · 1801.03217

Reduced critical processes for small populations

Minzhi Liu·Vladimir Vatutin

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Abstract

Let $\left\{ Z(n),n\geq 1\right\} $ be a critical Galton-Watson branching process with finite variance for the offspring size of particles. Assuming that $0 0$ or $\varphi (n)=o(n)$ as $n\rightarrow \infty $, we study the structure of the process $% \left\{ Z(m,n),0\leq m\leq n\right\} ,$ where $Z(m,n)$ is the number of particles in the process at moment $m\leq n$ having a positive number of descendants at moment $n$.

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Minzhi Liu, Vladimir Vatutin. 2018-01-10. Reduced critical processes for small populations. https://arxiv.org/abs/1801.03217

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