HEAVY-TAILED BRANCHING PROCESS WITH IMMIGRATION

被引：11

作者：

Basrak, Bojan ^{[1
]}

Kulik, Rafal ^{[2
]}

Palmowski, Zbigniew ^{[3
]}

机构：

[1] Univ Zagreb, Dept Math, Zagreb 10000, Croatia

[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON, Canada

[3] Univ Wroclaw, Math Inst, PL-50138 Wroclaw, Poland

来源：

STOCHASTIC MODELS | 2013年 / 29卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Branching process with immigration; INAR; Regularly varying distribution; 60G51; 60G50; 60K25; GALTON-WATSON PROCESS; RANDOM-VARIABLES; LIMIT-THEOREM; CONVERGENCE; SERIES; SUMS;

D O I：

10.1080/15326349.2013.838508

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：

In this article, we analyze a branching process with immigration defined recursively by X-t=(t) o Xt-1+B-t for a sequence (B-t) of i.i.d. random variables and random mappings theta(t) o x := theta(t)(x) = Sigma(x)(i=1) A(i)((t)), with (A(i)((t)))(i is an element of N0) being a sequence of N-0-valued i.i.d. random variables independent of B-t. We assume that one of generic variables A and B has a regularly varying tail distribution. We identify the tail behavior of the distribution of the stationary solution X-t. We also prove CLT for the partial sums that could be further generalized to FCLT. Finally, we also show that partial maxima have a Frechet limiting distribution.

引用

页码：413 / 434

页数：22

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