Convergence to a self-normalized G-Brownian motion  

作　　者：Zhengyan Lin Li-Xin Zhang 

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

出　　处：《Probability, Uncertainty and Quantitative Risk》2017年第1期87-111,共25页概率、不确定性与定量风险（英文）

基　　金：Research supported by Grants from the National Natural Science Foundation of China(No.11225104);the 973 Program(No.2015CB352302)and the Fundamental Research Funds for the Central Universities.

摘　　要：G-Brownian motion has a very rich and interesting new structure that nontrivially generalizes the classical Brownian motion.Its quadratic variation process is also a continuous process with independent and stationary increments.We prove a self-normalized functional central limit theorem for independent and identically distributed random variables under the sub-linear expectation with the limit process being a G-Brownian motion self-normalized by its quadratic variation.To prove the self-normalized central limit theorem,we also establish a new Donsker’s invariance principle with the limit process being a generalized G-Brownian motion.

关 键 词：Sub-linear expectation G-Brownian motion Central limit theorem Invariance principle SELF-NORMALIZATION 

分 类 号：O17[理学—数学]