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Normal approximation by Stein's method under sublinear expectations

文献类型：期刊论文

作者Song, Yongsheng1,2
刊名STOCHASTIC PROCESSES AND THEIR APPLICATIONS
出版日期2020-05-01
卷号130期号:5页码:2838-2850
ISSN号0304-4149
关键词Stein's method Normal approximation Sublinear expectation G-normal distribution
DOI10.1016/j.spa.2019.08.005
英文摘要Peng (2008) proved the Central Limit Theorem under a sublinear expectation: Let (X-i)(i >= 1) be a sequence of i.i.d random variables under a sublinear expectation (E) over cap with (E) over cap [X-1] = (E) over cap[-X-1] = 0 and (E) over cap [1X(1)vertical bar(3)] < infinity. Setting W-n := X-1+...+X-n/root n we have, for each bounded Lipschitz function phi, lim(n ->infinity) vertical bar<(E)over cap>[phi(W-n)] - N-G(phi)vertical bar = 0, where N-G is the G-normal distribution with G(a) = 1/2 (E) over cap [aX(1)(2)], a is an element of R In this paper, we shall give an estimate of the convergence rate of this CLT by Stein's method under sublinear expectations: Under the same conditions as above, there exists a constant a is an element of (0, 1) depending on (sigma) under bar and (sigma) over bar and a positive constant C-alpha,C-G depending on alpha, (sigma) under bar and (sigma) over bar such that sup&(VERBAR;phi vertical bar <= 1) vertical bar(E) over cap[phi(W-n)] - N-G(phi) vertical bar <= C-alpha,C-G (E) over cap[vertical bar X-1 vertical bar(2+alpha)]/n(alpha/2), where (sigma) over bar (2) = (E) over cap [X-1(2)], (sigma) under bar (2) = -(E) over cap [X-(2)(1)] > 0 and N-G is the G-normal distribution with G(a) = 1/2 (E) over cap [aX(1)(2)] = 1/2 ((sigma) over bar (2) a(+) - (sigma) under bar (2)a(-)), a is an element of R. (C) 2019 Elsevier B.V. All rights reserved.
资助项目NSFCs[11871458] ; NSFCs[11688101] ; Key Research Program of Frontier Sciences, CAS[QYZDB-SSW-SYS017] ; National Key R&D Program of China[2018YFA0703901] ; National Center for Mathematics and Interdisciplinary Sciences, CAS
WOS研究方向Mathematics
语种英语
出版者ELSEVIER
WOS记录号WOS:000528486200010
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/51333]  
专题应用数学研究所
通讯作者Song, Yongsheng
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, RCSDS, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式
GB/T 7714		 Song, Yongsheng. Normal approximation by Stein's method under sublinear expectations[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,2020,130(5):2838-2850.
APA Song, Yongsheng.(2020).Normal approximation by Stein's method under sublinear expectations.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,130(5),2838-2850.
MLA Song, Yongsheng."Normal approximation by Stein's method under sublinear expectations".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 130.5(2020):2838-2850.

入库方式： OAI收割

来源：数学与系统科学研究院

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