Harmonic moments, large and moderate deviation principles for Mandelbrot's cascade in a random environment

被引：6
作者：
Li, Yingqiu [1 ]
Liu, Quansheng [2 ]
Peng, Xuelian [1 ,3 ]
机构：
[1] Changsha Univ sci & Technol, Sch Math, Changsha 410114, Hunan, Peoples R China
[2] Univ Bretagne Sud, UMR 6205, LMBA, F-56000 Vannes, France
[3] Wuhan Qingchuan Univ, Dept Publ Studies, Wuhan 430204, Hubei, Peoples R China
来源：
STATISTICS & PROBABILITY LETTERS | 2019年 / 147卷
基金：
中国国家自然科学基金;
关键词：
Mandelbrot's cascade; Branching random walk; Random environment; Harmonic moments; Large deviations; Moderate deviations; CENTRAL LIMIT-THEOREMS; BRANCHING RANDOM-WALK; CONVERGENCE;
D O I：
10.1016/j.spl.2018.10.002
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：
For Mandelbrot's cascade in a random environment, we find the critical value for the existence of harmonic moments of the limit variable of Mandelbrot's martingale, and establish large and moderate deviation principles for the free energy. As applications, we show the corresponding limit theorems for branching random walks in random environments. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：57 / 65
页数：9
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