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Limit theorems with rate of convergence under sublinear expectations
Fang, Xiao1; Peng, Shige2; Shao, Qi-Man1; Song, Yongsheng3
2019-11-01
Source PublicationBERNOULLI
ISSN1350-7265
Volume25Issue:4APages:2564-2596
AbstractUnder the sublinear expectation E[.] := sup(theta is an element of Theta) E-theta[.] for a given set of linear expectations {E-theta : theta is an element of Theta}, we establish a new law of large numbers and a new central limit theorem with rate of convergence. We present some interesting special cases and discuss a related statistical inference problem. We also give an approximation and a representation of the G-normal distribution, which was used as the limit in Peng's (Law of large numbers and central limit theorem under nonlinear expectations (2007) Preprint) central limit theorem, in a probability space.
Keywordcentral limit theorem G-normal distribution law of large numbers rate of convergence Stein's method sublinear expectation
DOI10.3150/18-BEJ1063
Language英语
Funding ProjectCUHK ; NSF[11626247] ; Hong Kong RGC[GRF 14302515] ; Hong Kong RGC[14304917] ; NCMIS, NSFC[11688101] ; Key Research Program of Frontier Sciences, CAS[QYZDB-SSW-SYS017]
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000485825100006
PublisherINT STATISTICAL INST
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35629
Collection应用数学研究所
Corresponding AuthorFang, Xiao
Affiliation1.Chinese Univ Hong Kong, Dept Stat, Shatin, Hong Kong, Peoples R China
2.Shandong Univ, Inst Math, Jinan 250100, Shandong, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Fang, Xiao,Peng, Shige,Shao, Qi-Man,et al. Limit theorems with rate of convergence under sublinear expectations[J]. BERNOULLI,2019,25(4A):2564-2596.
APA Fang, Xiao,Peng, Shige,Shao, Qi-Man,&Song, Yongsheng.(2019).Limit theorems with rate of convergence under sublinear expectations.BERNOULLI,25(4A),2564-2596.
MLA Fang, Xiao,et al."Limit theorems with rate of convergence under sublinear expectations".BERNOULLI 25.4A(2019):2564-2596.
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