Uniqueness, Extinction and Explosivity of Generalised Markov Branching Processes with Pairwise Interaction

被引：8

作者：

Chen, Anyue ^{[1
,2
]}

Pollett, Phil ^{[3
]}

Li, Junping ^{[4
]}

Zhang, Hanjun ^{[5
]}

机构：

[1] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England

[2] Univ Hong Kong, Dept Stat & Actuarial Sci, Pokfulam, Hong Kong, Peoples R China

[3] Univ Queensland, Dept Math, Brisbane, Qld 4072, Australia

[4] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China

[5] Xiangtan Univ, Sch Math & Comp Sci, Xiangtan 411105, Peoples R China

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2010年 / 12卷 / 03期

基金：

澳大利亚研究理事会; 中国国家自然科学基金;

关键词：

Markov branching process; Pairwise interaction; Regularity; Uniqueness; Extinction; Explosion; Hitting times; Renewal sequence;

D O I：

10.1007/s11009-009-9121-y

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：

We examine basic properties regarding uniqueness, extinction, and explosivity for the generalised Markov branching processes with pairwise interaction. First we establish uniqueness criteria, proving that in the essentially-explosive case the process is honest if and only if the mean death rate is greater than or equal to the mean birth rate, while in the sub-explosive case the process is dishonest only in exceptional circumstances. Explicit expressions are then obtained for the extinction probabilities, the mean extinction times and the conditional mean extinction times. Explosivity is also investigated and an explicit expression for mean explosion time is established.

引用

页码：511 / 531

页数：21

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Phil Pollett
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