The survival probability of critical and subcritical branching processes in finite state space Markovian environment

被引：4

作者：

Grama, Ion ^{[1
]}

Lauvergnat, Ronan ^{[1
]}

Le Page, Emile ^{[1
]}

机构：

[1] Univ Bretagne Sud, CNRS, UMR 6205, LMBA, Vannes, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2019年 / 129卷 / 07期

关键词：

Critical and subcritical branching process; Random environment; Markov chain; Survival probability; LIMIT-THEOREMS;

D O I：

10.1016/j.spa.2018.07.016

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：

Let (Z(n))(n >=)(0) be a branching process in a random environment defined by a Markov chain (X-n)(n >= 0) with values in a finite state space X. Let P-i be the probability law generated by the trajectories of (X-n)(n >= 0) starting at X-0 = i is an element of X. We study the asymptotic behaviour of the joint survival probability P-i (Z(n) > 0, X-n = j), j is an element of X as n -> +infinity in the critical and strongly, intermediate and weakly subcritical cases. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：2485 / 2527

页数：43

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