Limit Theorems for Critical Galton-Watson Processes with Immigration Stopped at Zero

被引：0
作者：
Dou Dou Li
Mei Zhang
Xian Yu Zhang
机构：
[1] Beijing University of Technology,College of Statistics and Data Science, Faculty of Science
[2] Beijing Normal University,Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences
来源：
Acta Mathematica Sinica, English Series | 2024年 / 40卷
关键词：
Branching; immigration; critical; life period; limit theorems; 60J80; 60F10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider a critical Galton–Watson branching process with immigration stopped at zero W. Some precise estimation on the probability generating function of the n-th population are obtained, and the tail probability of the life period of W is studied. Based on above results, two conditional limit theorems for W are established.
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页码：435 / 450
页数：15
相关论文
共 27 条
[1]  
Badalbaev I S(1983)Lifetimes of an Izv. Akad. Nauk Uzssr, Ser. Fiz., Mat. Nauk. 2 7-13
[2]  
Mashrabbaev A(2020) > 1-type Galton–Watson process with immigration J. Appl. Probab. 57 237-249
[3]  
Dyakonova E(1985)Branching processes in random environment with immigration stopped at zero J. Appl. Probab. 22 223-227
[4]  
Li D D(2010)The critical branching process with immigration stopped at zero Geophys. J. Int. 180 1313-1328
[5]  
Vatutin V(1966)Statistical distributions of earthquake numbers: consequence of branching process Theory Probab. Appl. 11 513-540
[6]  
Ivanoff B G(2021)The Galton–Watson process with mean one and finite variance J. Theoret. Probab. 34 874-896
[7]  
Seneta E(2019)Subcritical branching processes in random environment with immigration stopped at zero Acta Math. Sinica. 35 537-549
[8]  
Kagan Y Y(2021)Asymptotic behaviors for critical branching processes with immigration Sci. China Math. 64 1885-1904
[9]  
Kesten H(1972)Harmonic moments and large deviations for a critical Galton–Watson process with immigration J. Aust. Math. Soc. 13 277-290
[10]  
Ney P(1975)Further results on the critical Galton–Watson process with immigration Math. Biosci. 26 1-18
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