Measure concentration through non-Lipschitz observables and functional inequalities

被引：1

作者：

Guillin, Arnaud ^{[1
]}

Joulin, Alderic ^{[2
]}

机构：

[1] Univ Blaise Pascal, Clermont Ferrand II, France

[2] Univ Toulouse, Inst Math Toulouse, Toulouse, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2013年 / 18卷

关键词：

Concentration; invariant measure; reversible Markov process; Lyapunov condition; functional inequality; carre du champ; diffusion process; jump process; LOGARITHMIC SOBOLEV INEQUALITIES; SPECTRAL GAP; DEVIATION INEQUALITIES; POINCARE INEQUALITY; ENTROPY DECAY; INFORMATION;

D O I：

10.1214/EJP.v18-2425

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：

Non-Gaussian concentration estimates are obtained for invariant probability measures of reversible Markov processes. We show that the functional inequalities approach combined with a suitable Lyapunov condition allows us to circumvent the classical Lipschitz assumption of the observables. Our method is general and offers an unified treatment of diffusions and pure-jump Markov processes on unbounded spaces.

引用

页码：1 / 26

页数：26

共 42 条

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Aida S, 1994, MATH RES LETT, V1, P75

[2]

[Anonymous], 2005, THESIS GEORGIA I TEC

[3] A simple proof of the Poincare inequality for a large class of probability measures including the log-concave case [J].