Subcritical branching processes in a random environment without the Cramer condition

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Vatutin, Vladimir²  Zheng, Xinghua¹ 

[1] Hong Kong Univ Sci & Technol, Dept ISOM, Kowloon, Hong Kong, Peoples R China

[2] Steklov Math Inst, Dept Discrete Math, Moscow 119991, Russia

关键词: Branching process;    Random environment;    Random walk;    Survival probability;    Functional limit theorem;   

DOI  :  10.1016/j.spa.2012.04.008

来源: Elsevier

【 摘 要 】

A subcritical branching process in random environment (BPRE) is considered whose associated random walk does not satisfy the Cramer condition. The asymptotics for the survival probability of the process is investigated, and a Yaglom type conditional limit theorem is proved for the number of particles up to moment n given survival to this moment. Contrary to other types of subcritical BPRE, the limiting distribution is not discrete. We also show that the process survives for a long time owing to a single big jump of the associate random walk accompanied by a population explosion at the beginning of the process. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free