WEAKLY SUPERCRITICAL BRANCHING PROCESS IN A RANDOM ENVIRONMENT DYING AT A DISTANT MOMENT

被引:0
作者
Afanasyev, V. I. [1 ]
机构
[1] Russian Acad Sci, Steklov Math Inst, Moscow, Russia
基金
俄罗斯科学基金会;
关键词
weakly supercritical branching process in a random environment; conditional functional limit theorems; LIMIT-THEOREMS;
D O I
10.1137/S0040585X97T991611
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 functional limit theorem is proved for a weakly supercritical branching process in a random environment under the condition that the process becomes extinct after time n -> infinity.
引用
收藏
页码:537 / 558
页数:22
相关论文
共 9 条
[1]   Limit Theorems for Weakly Subcritical Branching Processes in Random Environment [J].
Afanasyev, V. I. ;
Boeinghoff, C. ;
Kersting, G. ;
Vatutin, V. A. .
JOURNAL OF THEORETICAL PROBABILITY, 2012, 25 (03) :703-732
[2]  
AFANASYEV V. I., 2022, Diskr. Mat., V34, P3, DOI [10.4213/dm1724, DOI 10.4213/DM1724]
[3]   Criticality for branching processes in random environment [J].
Afanasyev, VI ;
Geiger, J ;
Kersting, G ;
Vatutin, VA .
ANNALS OF PROBABILITY, 2005, 33 (02) :645-673
[4]  
AFANASYEV VI, 1998, DISCRET MATH APPL, V8, P35, DOI DOI 10.1515/DMA.1998.8.1.35
[5]   BRANCHING PROCESSES WITH RANDOM ENVIRONMENTS .1. EXTINCTION PROBABILITIES [J].
ATHREYA, KB ;
KARLIN, S .
ANNALS OF MATHEMATICAL STATISTICS, 1971, 42 (05) :1499-+
[6]   Small positive values for supercritical branching processes in random environment [J].
Bansaye, Vincent ;
Boeinghoff, Christian .
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2014, 50 (03) :770-805
[8]  
Geiger J, 2003, ANN I H POINCARE-PR, V39, P593, DOI [10.1016/S0246-0203(02)00020-1, 10.1016/S0246-0203(02)00020-1/FLA]
[9]  
[No title captured]