Small value probabilities for supercritical branching processes with immigration

被引：7

作者：

Chu, Weijuan ^{[1
,2
]}

Li, Wenbo V. ^{[3
]}

Ren, Yan-Xia ^{[1
,4
]}

机构：

[1] Peking Univ, LMAM, Sch Math Sci, Beijing 100871, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[4] Peking Univ, Ctr Stat Sci, Beijing 100871, Peoples R China

来源：

BERNOULLI | 2014年 / 20卷 / 01期

基金：

高等学校博士学科点专项科研基金;

关键词：

immigration; small value probability; supercritical Galton-Watson branching process; GALTON-WATSON PROCESSES; GAUSSIAN-PROCESSES; BROWNIAN-MOTION; TIME;

D O I：

10.3150/12-BEJ490

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：

We consider a supercritical Galton-Watson branching process with immigration. It is well known that under suitable conditions on the offspring and immigration distributions, there is a finite, strictly positive limit W for the normalized population size. Small value probabilities for W are obtained. Precise effects of the balance between offspring and immigration distributions are characterized.

引用

页码：377 / 393

页数：17

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