arXiv subjects

Huizi Yao

Publications and source records attributed to Huizi Yao.

2 recordsLinked to original sources

arXiv2021

Two-type linear fractional branching processes in varying environments with asymptotically constant mean matrices

Consider two-type linear-fractional branching processes in varying environments with asymptotically constant mean matrices. Let $ν$ be the extinction time. Under certain conditions, we show that both $P(ν=n)$ and $P(ν>n)$ are asymptotically the same as some functions of the products of spectral radii of the mean matrices. We also give an example for which $P(ν=n)$ decays with various speeds such as $\frac{c}{n(\log n)^2},$ $\frac{c}{n^β},β>1$ et al. which are very different from the ones of homogeneous multitype Galton-Watson processes.

math.PR↗

arXiv2019

Coalescence for supercritical Galton-Watson processes with immigration

In this paper, we consider Galton-Watson processes with immigration. Pick $i(\ge2)$ individuals randomly without replacement from the $n$-th generation and trace their lines of descent back in time till they coalesce into $1$ individual in a certain generation, which we denote by $X_{i,1}^n$ and is called the coalescence time. Firstly, we give the probability distribution of $X_{i,1}^n$ in terms of the probability generating functions of both the offspring distribution and the immigration law. Then by studying the limit behaviors of various functionals of the Galton-Watson process with immigration, we find the limit distribution of $X_{2,1}^n$ as $n\rightarrow\infty.$

math.PR↗