Self-Normalized Moderate Deviation and Laws of the Iterated Logarithm Under G-Expectation  

作　　者：Li-Xin Zhang 

机构地区：[1]Department of Mathematics,Zhejiang University,Hangzhou 310027,China

出　　处：《Communications in Mathematics and Statistics》2016年第2期229-263,共35页数学与统计通讯（英文）

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

摘　　要：The sub-linear expectation or called G-expectation is a non-linear expectation having advantage of modeling non-additive probability problems and the volatilityuncertainty in finance.Let{Xn;n≥1}be a sequence of independent random vari-ables in a sub-linear expectation space(Ω,H,E^(^)).Denote S_(n)=∑_(k=1)^(n)Xk and=V_(n)^(2)=∑_(k=1)^(n)X_(k)^(2).In this paper,a moderate deviation for self-normalized sums,thatis,the asymptotic capacity of the event{Sn/Vn≥x_(n)}for x_(n)=o(√n),is found both for identically distributed random variables and independent but not necessarilyidentically distributed random variables.As an application,the self-normalized lawsof the iterated logarithm are obtained.A Bernstein's type inequality is also establishedfor proving the law of the iterated logarithm.

关 键 词：Non-linear expectation Capacity SELF-NORMALIZATION Law of theiterated logarithm Moderate deviation 

分 类 号：O17[理学—数学]