Logarithmic Sobolev inequalities for some nonlinear PDE's

被引：81

作者：

Malrieu, F ^{[1
]}

机构：

[1] Univ Toulouse 3, Lab Stat & Probabil, UMR C5583, F-31064 Toulouse, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2001年 / 95卷 / 01期

关键词：

interacting particle system; logarithmic Sobolev inequality; propagation of chaos; relative entropy; concentration of measure;

D O I：

10.1016/S0304-4149(01)00095-3

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The aim of this paper is to study the behavior of solutions of some nonlinear partial differential equations of Mac Kean-Vlasov type. The main tools used are, on one hand, the logarithmic Sobolev inequality and its connections with the concentration of measure and the transportation inequality with quadratic cost; on the other hand, the propagation of chaos for particle systems in mean field interaction. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：109 / 132

页数：24

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