非线性概率下行内负相协随机变量阵列的对数律  

Laws of the logarithm for arrays of rowwise negatively associated random variables under nonlinear probabilities

作　　者：兰玉婷 冯新伟 Yuting Lan;Xinwei Feng

机构地区：[1]上海财经大学统计与管理学院,上海200433 [2]香港中文大学统计系,香港

出　　处：《中国科学：数学》2019年第8期1087-1102,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11601280)资助项目

摘　　要：本文在上概率空间中给出随机变量负相协的定义,该定义弱于现有非线性概率下的某些独立性概念.在此框架下,本文通过对随机变量阵列收敛性质的研究,得到上概率下行内负相协随机变量阵列的对数律,并同时给出依容度收敛的弱对数律.In this paper, the notion of negatively associated random variables is introduced under nonlinear probabilities, which is weaker than some existing conditions of independence. Within this framework, a law of the logarithm for arrays of rowwise negatively associated random variables is established by investigating their convergence properties. In addition, a weak law of the logarithm with the convergence of capacity is obtained.

关 键 词：非线性概率 负相协随机变量 对数律 随机变量阵列 

分 类 号：O211.4[理学—概率论与数理统计]