Lipschitzian norm estimate of one-dimensional Poisson equations and applications

doi:10.1214/10-AIHP360

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	Lipschitzian norm estimate of one-dimensional Poisson equations and applications
	Djellout, Hacene 1; Wu, Liming 1,2
	2011-05-01
发表期刊	ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
ISSN	0246-0203
卷号	47 期号:2 页码:450-465
摘要	By direct calculus we identify explicitly the Lipschitzian norm of the solution of the Poisson equation - LG = g in terms of various norms of g, where L is a Sturm-Liouville operator or generator of a non-singular diffusion in an interval. This allows us to obtain the best constant in the L(1)-Poincare inequality (a little stronger than the Cheeger isoperimetric inequality) and some sharp transportation information inequalities and concentration inequalities for empirical means. We conclude with several illustrative examples.
关键词	Poisson equations Transportation-information inequalities Concentration and isoperimetric inequalities
DOI	10.1214/10-AIHP360
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000289654500006
出版者	INST MATHEMATICAL STATISTICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12411
专题	中国科学院数学与系统科学研究院
通讯作者	Djellout, Hacene
作者单位	1.Univ Clermont Ferrand, CNRS, Math Lab, UMR 6620, F-63177 Clermont Ferrand, France 2.Acad China, Inst Appl Math, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Djellout, Hacene,Wu, Liming. Lipschitzian norm estimate of one-dimensional Poisson equations and applications[J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,2011,47(2):450-465.
APA	Djellout, Hacene,&Wu, Liming.(2011).Lipschitzian norm estimate of one-dimensional Poisson equations and applications.ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,47(2),450-465.
MLA	Djellout, Hacene,et al."Lipschitzian norm estimate of one-dimensional Poisson equations and applications".ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 47.2(2011):450-465.