标题：EXTENSION OF THE STRONG LAW OF LARGE NUMBERS FOR CAPACITIES
作者：Chen, Zengjing; Huang, Weihuan; Wu, Panyu
作者机构：[Chen, Zengjing] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.; [Huang, Weihuan; Wu, Panyu] Shandong Univ, Zhongtai Secur Inst F 更多
通讯作者地址：[Wu, PY]Shandong Univ, Zhongtai Secur Inst Financial Studies, Jinan 250100, Shandong, Peoples R China.
来源：MATHEMATICAL CONTROL AND RELATED FIELDS
关键词：Capacity; law of large numbers; independence; upper expectation
摘要：In this paper, with a new notion of exponential independence for random variables under an upper expectation, we establish a kind of strong laws of large numbers for capacities. Our limit theorems show that the cluster points of empirical averages not only lie in the interval between the upper expectation and the lower expectation with lower probability one, but such an interval also is the unique smallest interval of all intervals in which the limit points of empirical averages lie with lower probability one. Furthermore, we also show that the cluster points of empirical averages could reach the upper expectation and lower expectation with upper probability one.