Moments, moderate and large deviations for a branching process in a random environment

被引：42

作者：

Huang, Chunmao

Liu, Quansheng ^{[1
]}

机构：

[1] Univ Bretagne Sud, LMAM, F-56017 Vannes, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Branching process; Random environment; Moments; Harmonic moments; Large deviation; Moderate deviation; Central limit theorem; ASYMPTOTIC PROPERTIES; LIMIT-THEOREMS;

D O I：

10.1016/j.spa.2011.09.001

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)) be a supercritical branching process in a random environment and W be the limit of the normalized population size Z(n)/E[Z(n)vertical bar xi]. We show large and moderate deviation principles for the sequence log Z(n) (with appropriate normalization). For the proof, we calculate the critical value for the existence of harmonic moments of W, and show an equivalence for all the moments of Z(n). Central limit theorems on W - W-n and log Z(n) are also established. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：522 / 545

页数：24

共 26 条

[1] Functional limit theorems for strongly subcritical branching processes in random environment [J].