arXiv
Open Access
2019
Coalescence for supercritical Galton-Watson processes with immigration
Hua-Ming Wang
Lulu Li
Huizi Yao
Abstrak
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 $n\rightarrow\infty.$
Topik & Kata Kunci
Penulis (3)
H
Hua-Ming Wang
L
Lulu Li
H
Huizi Yao
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2019
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓