MULTI-TYPE BRANCHING PROCESSES WITH TIME-DEPENDENT BRANCHING RATES

被引：11

作者：

Dolgopyat, D. ^{[1
]}

Hebbar, P. ^{[1
]}

Koralov, L. ^{[1
]}

Perlman, M. ^{[2
]}

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

JOURNAL OF APPLIED PROBABILITY | 2018年 / 55卷 / 03期

基金：

美国国家科学基金会;

关键词：

Multi-type branching; extinction probability; nonnegative matrix product; exponential limit law;

D O I：

10.1017/jpr.2018.46

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：

Under mild nondegeneracy assumptions on branching rates in each generation, we provide a criterion for almost sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total number of particles (conditioned on survival and divided by the expectation of the resulting random variable) to approach an exponential random variable as time goes to infinity.

引用

页码：701 / 727

页数：27

共 23 条

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