Sanov's theorem in the Wasserstein distance: A necessary and sufficient condition

doi:10.1016/j.spl.2009.12.003

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	Sanov's theorem in the Wasserstein distance: A necessary and sufficient condition
	Wang, Ran 1; Wang, Xinyu 1; Wu, Liming 2,3
	2010-03-01
发表期刊	STATISTICS & PROBABILITY LETTERS
ISSN	0167-7152
卷号	80 期号:5-6 页码:505-512
摘要	Let (X(n))(n >= 1) be a sequence of i.i.d.r.v.'s with values in a Polish space (E, d) of law mu. Consider the empirical measures L(n) = 1/n Sigma(n)(k=1) delta(Xk), n >= 1. Our purpose is to generalize Sanov's theorem about the large deviation principle of L(n) from the weak convergence topology to the stronger Wasserstein metric W(p). We show that L(n) satisfies the large deviation principle in the Wasserstein metric W(p) (p is an element of [1, +infinity)) if and only if integral(E) e(lambda dp(x0, x))d mu(x) < +infinity for all lambda > 0, and for some x(0) is an element of E. (C) 2009 Elsevier B.V. All rights reserved.
DOI	10.1016/j.spl.2009.12.003
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000274946100032
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11200
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Ran
作者单位	1.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China 2.Univ Clermont Ferrand, Lab Math Appl, CNRS, UMR 6620, F-63177 Aubiere, France 3.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang, Ran,Wang, Xinyu,Wu, Liming. Sanov's theorem in the Wasserstein distance: A necessary and sufficient condition[J]. STATISTICS & PROBABILITY LETTERS,2010,80(5-6):505-512.
APA	Wang, Ran,Wang, Xinyu,&Wu, Liming.(2010).Sanov's theorem in the Wasserstein distance: A necessary and sufficient condition.STATISTICS & PROBABILITY LETTERS,80(5-6),505-512.
MLA	Wang, Ran,et al."Sanov's theorem in the Wasserstein distance: A necessary and sufficient condition".STATISTICS & PROBABILITY LETTERS 80.5-6(2010):505-512.