arXiv subjects

Minzhi Liu

Publications and source records attributed to Minzhi Liu.

2 recordsLinked to original sources

arXiv2018

Reduced critical processes for small populations

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 $φ(n)=o(n)$ 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 $n$.

math.PR↗

arXiv2017

Limit theorems for supercritical MBPRE with linear fractional offspring distributions

We investigate the limit behavior of supercritical multitype branching processes in random environments with linear fractional offspring distributions and show that there exists a phase transition in the behavior of local probabilites of the process affected by strongly and intermediately supercritical regimes. Some conditional limit theorems can also be obtained from the representation of generating functions.

math.PR↗