检索结果-南通市图书馆

Poincaréand Logarithmic Sobolev Inequalities for Nearly Radial Measures

Acta Mathematica Sinica,English Series 2022年第8期38卷 1377-1398页

作者： Patrick CATTIAUX arnaud guillin Li Ming WU Institut de Mathématiques de Toulouse CNRS UMR 5219UniversitéPaul Sabatier118 Route de NarbonneF-31062 Toulouse Cedex 09 Laboratoire de Mathématiques Blaise Pascal CNRS UMR 6620UniversitéClermont-AuvergneAvenue des LandaisF-63177 Aubiere

Poincaréinequality has been studied by Bobkov for radial measures,but few are known about the logarithmic Sobolev inequality in the radial case.We try to fill this gap here using different methods:Bobkov's argument and super-Poincaréinequalities,direct approach via L_(1)-logarithmic Sobolev inequalities.We also give various examples where the obtained bounds are quite sharp.Recent bounds obtained by Lee–Vempala in the log-concave bounded case are refined for radial measures.

关键词： Radial measure log-concave measure Poincaréinequality logarithmic Sobolev inequality super-Poincaréinequality

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

On the Simpson index for the Wright–Fisher process with random selection and immigration

引用

International Journal of Biomathematics 2020年第6期13卷 77-111页

作者： arnaud guillin Franck Jabot arnaud Personne Laboratoire d'Ingdnierie pour les Systemes Complexes IRSTEA Campus des Cezeaux 9 avenue Blaise Pascal-CS *** AubiereFrance

Moran or Wright–Fisher processes are probably the most well known models to study the evolution of a population under environmental various effects.Our object of study will be the Simpson index which measures the level of diversity of the population,one of the key parameters for ecologists who study for example,forest dynamics.Following ecological motivations,we will consider,here,the case,where there are various species with fitness and immigration parameters being random processes(and thus time evolving).The Simpson index is difficult to evaluate when the population is large,except in the neutral(no selection)case,because it has no closed formula.Our approach relies on the large population limit in the“weak”selection case,and thus to give a procedure which enables us to approximate,with controlled rate,the expectation of the Simpson index at fixed time.We will also study the long time behavior(invariant measure and convergence speed towards equilibrium)of the Wright–Fisher process in a simplified setting,allowing us to get a full picture for the approximation of the expectation of the Simpson index.

关键词： Simpson index multidimensional Wright-Fisher process random selection random immigration moment’s closure

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

PENALIZED LEAST SQUARE IN SPARSE SETTING WITH CONVEX PENALTY AND NON GAUSSIAN ERRORS

引用

Acta Mathematica Scientia 2021年第6期41卷 2198-2216页

作者： Doualeh ABDILLAHI-ALI Nourddine AZZAOUI arnaud guillin Guillaume LE MAILLOUX Tomoko MATSUI Laboratoire de Mathématiques Blaise Pascal CNRS-UMR 6620Université Clermont-Auvergne(UCA)63000Clermont-FerrandFrance Department of Statistical Modeling Institute of Statistical Mathematics10-3 Midori-choTachikawa-shiTokyo1908562Japan

This paper consider the penalized least squares estimators with convex penalties or regularization norms.We provide sparsity oracle inequalities for the prediction error for a general convex penalty and for the particular cases of Lasso and Group Lasso estimators in a regression setting.The main contribution is that our oracle inequalities are established for the more general case where the observations noise is issued from probability measures that satisfy a weak spectral gap(or Poincaré)inequality instead of Gaussian distributions.We illustrate our results on a heavy tailed example and a sub Gaussian one;we especially give the explicit bounds of the oracle inequalities for these two special examples.

关键词： penalized least squares Gaussian errors convex penalty

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Poincaré and Logarithmic Sobolev inequalities for nearly radial measures

引用

Acta Mathematica Sinica,English Series 2021年

作者： Patrick CATTIAUX arnaud guillin Liming WU Institut de Mathématiques de Toulouse.CNRS UMR 5219.Université Paul Sabatier Laboratoire de Mathématiques Blaise Pascal CNRS UMR 6620 Université Clermont-Auvergne

Poincaré inequality has been studied by Bobkov for radial measures, but few is known about the logarithmic Sobolev inequality in the radial case. We try to fill this gap here using different methods: Bobkov’s argument and super-Poincare′ inequalities, direct approach via L1-logarithmic Sobolev inequalities. We also give various examples where the obtained bounds are quite sharp. Recent bounds obtained by Lee-Vempala in the log-concave bounded case are refined for radial measures.

关键词： radial measure log-concave measure Poincaré inequality logarithmic Sobolev inequality SuperPoincaré inequality

来源：

同方期刊数据库评论

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

欢迎您,

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

在线全文

在线全文

请选择保存的检索档案：

请选择收藏分类：

通借通还

欢迎您,

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

在线全文

在线全文

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：