Limit Theorems for a Supercritical Branching Process with Immigration at Zero in a Random Environment

被引：0

作者：

Zhao, Yinxuan ^{[1
,2
]}

Li, Doudou ^{[3
]}

Zhang, Mei ^{[1
,2
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Beijing Normal Univ, Lab Math & Complex Syst, Beijing 100875, Peoples R China

[3] Beijing Univ Technol, Coll Stat & Data Sci, Fac Sci, Beijing 100124, Peoples R China

来源：

MARKOV PROCESSES AND RELATED FIELDS | 2023年 / 29卷 / 05期

基金：

中国国家自然科学基金;

关键词：

branching process; immigration; random environment; state dependent; supercritical; linear fractional;

D O I：

10.61102/1024-2953-mprf.2023.29.5.003

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let Z be a supercritical branching process with immigration at zero in a random environment, where the immigration is allowed entering a generation iff the previous generation is empty. The limit theorems for the naturally normalized population size Wn shall be investigated, under both the annealed law and quenched law. In addition, in the linear fractional case, the harmonic moments of W and the convergence rate of the transition probabilities p(n) l,j of Z are studied.

引用

页码：661 / 681

页数：110

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