Functional Shige Peng’s Central Limit Theorems for Martingale Vectors  

作　　者：Li-Xin Zhang 

机构地区：[1]School of Mathematical Sciences,Zhejiang University,Hangzhou 310027,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2024年第2期357-383,共27页数学与统计通讯（英文）

基　　金：Supported by grants from the NSF of China(Grant No.11731012,12031005);Ten Thousands Talents Plan of Zhejiang Province(Grant No.2018R52042);NSF of Zhejiang Province(Grant No.LZ21A010002);the Fundamental Research Funds for the Central Universities.

摘　　要：In this paper,the functional central limit theorem is established for martingale like ran-dom vectors under the framework sub-linear expectations introduced by Shige Peng.As applications,the Lindeberg central limit theorem for independent random vectors is established,the sufficient and necessary conditions of the central limit theorem for independent and identically distributed random vectors are found,and a Lévy’s characterization of a multi-dimensional G-Brownian motion is obtained.

关 键 词：Random vector Central limit theorem Functional central limit theorem Martingale difference Sub-linear expectation 

分 类 号：O17[理学—数学]