Lipschitzian norm estimate of one-dimensional Poisson equations and applications

doi:10.1214/10-AIHP360

	Lipschitzian norm estimate of one-dimensional Poisson equations and applications
	Djellout, Hacene 1; Wu, Liming 1,2
刊名	ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
	2011-05-01
卷号	47 期号:2 页码:450-465
关键词	Poisson equations Transportation-information inequalities Concentration and isoperimetric inequalities
ISSN号	0246-0203
DOI	10.1214/10-AIHP360
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	INST MATHEMATICAL STATISTICS
WOS记录号	WOS:000289654500006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/12410]
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.