Branching processes in a random environment with immigration stopped at zero

被引：14

作者：

Dyakonova, Elena ^{[1
]}

Li, Doudou ^{[2
,3
]}

Vatutin, Vladimir ^{[1
,3
]}

Zhang, Mei ^{[2
,3
]}

机构：

[1] Steklov Math Inst, 8 Gubkin St, Moscow 119991, Russia

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

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

来源：

JOURNAL OF APPLIED PROBABILITY | 2020年 / 57卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

Branching process; random environment; immigration; life period; CONDITIONAL LIMIT-THEOREM; RANDOM-WALK; DISTRIBUTIONS;

D O I：

10.1017/jpr.2019.94

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：

A critical branching process with immigration which evolves in a random environment is considered. Assuming that immigration is not allowed when there are no individuals in the population, we investigate the tail distribution of the so-called life period of the process, i.e. the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time.

引用

页码：237 / 249

页数：13

共 22 条

[1] CONDITIONAL LIMIT THEOREM FOR THE MAXIMUM OF A RANDOM WALK IN RANDOM ENVIRONMENT
Afanasyev, V. I.
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 2014, 58 (04) : 525 - 545
[2] Limit Theorems for Weakly Subcritical Branching Processes in Random Environment
Afanasyev, V. I.
Boeinghoff, C.
Kersting, G.
Vatutin, V. A.
[J]. JOURNAL OF THEORETICAL PROBABILITY, 2012, 25 (03) : 703 - 732
[3] Criticality for branching processes in random environment
Afanasyev, VI
Geiger, J
Kersting, G
Vatutin, VA
[J]. ANNALS OF PROBABILITY, 2005, 33 (02) : 645 - 673
[4] Badalbaev I S., 1983, IZV AKAD NAUK UZ FMN, V2, P7
[5] Bingham NH., 1989, Regular variation
[6] FELLER W., 1971, An Introduction to Probability Theory and Its Applications, VII
[7] Haccou P., 2005, CAMB SER ADAPTIVE DY, V5
[8] Statistical distributions of earthquake numbers: consequence of branching process
Kagan, Yan Y.
[J]. GEOPHYSICAL JOURNAL INTERNATIONAL, 2010, 180 (03) : 1313 - 1328
[9] SOME RESULTS ABOUT MULTIDIMENSIONAL BRANCHING PROCESSES WITH RANDOM ENVIRONMENTS
KAPLAN, N
[J]. ANNALS OF PROBABILITY, 1974, 2 (03) : 441 - 455
[10] Kersting G., 2017, Discrete Time Branching Processes in Random Environment

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