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

被引：0

作者：

Anyue Chen

Phil Pollett

Junping Li

Hanjun Zhang

机构：

[1] The University of Liverpool,Department of Mathematical Sciences

[2] University of Hong Kong,Department of Statistics and Actuarial Science

[3] University of Queensland,Department of Mathematics

[4] Central South University,School of Mathematical Sciences and Computing Technology

[5] Xiangtan University,School of Mathematics and Computing Science

来源：

Methodology and Computing in Applied Probability | 2010年 / 12卷

关键词：

Markov branching process; Pairwise interaction; Regularity; Uniqueness; Extinction; Explosion; Hitting times; Renewal sequence; Primary 60J27; Secondary 60J80;

D O I：

暂无

中图分类号：

学科分类号：

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：20

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