On the survival probability of a branching process in a random environment

被引：21

作者：

DSouza, JC ^{[1
]}

Hambly, BM ^{[1
]}

机构：

[1] UNIV EDINBURGH, DEPT MATH & STAT, EDINBURGH EH9 3JZ, MIDLOTHIAN, SCOTLAND

来源：

ADVANCES IN APPLIED PROBABILITY | 1997年 / 29卷 / 01期

关键词：

branching processes; random environments; varying environments; Galton-Watson process; survival probability; random walks; extinction time; large deviations;

D O I：

10.2307/1427860

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 derive a variety of estimates for the survival probability of a branching process in a random environment. There are three cases of interest, the critical, weakly and strongly subcritical. The large deviation result, first obtained by Dekking for the class of finite state space i.i.d. environments, is shown to hold in more general environments. We also obtain some finer convergence results.

引用

页码：38 / 55

页数：18

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