Large deviations for empirical measures of mean-field Gibbs measures

被引：14

作者：

Liu, Wei ^{[1
,2
]}

Wu, Liming ^{[3
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] Wuhan Univ, Computat Sci Hubei Key Lab, Wuhan 430072, Hubei, Peoples R China

[3] Univ Clermont Auvergne, Lab Math Blaise Pascal, CNRS UMR 6620, 3 Pl Vasarely, F-63178 Aubiere, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2020年 / 130卷 / 02期

关键词：

Large deviations; Empirical measure; U-statistics; Interacting particle systems; McKean-Vlasov equation; Mean-field Gibbs measure; PRINCIPLE;

D O I：

10.1016/j.spa.2019.01.008

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：

In this paper, we show that the empirical measure of mean-field model satisfies the large deviation principle with respect to the weak convergence topology or the stronger Wasserstein metric, under the strong exponential integrability condition on the negative part of the interaction potentials. In contrast to the known results we prove this without any continuity or boundedness condition on the interaction potentials. The proof relies mainly on the law of large numbers and the exponential decoupling inequality of de la Pena for U-statistics. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：503 / 520

页数：18

共 50 条

[21] Large deviations for empirical measures of dense stochastic block graphs [J].

Zheng Wenhua ;

Liu Qun .

JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING, 2020,

[22] Large deviations for weighted empirical measures arising in importance sampling [J].

Hult, Henrik ;

Nyquist, Pierre .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2016, 126 (01) :138-170

[23] LARGE DEVIATIONS THEOREMS FOR EMPIRICAL MEASURES IN FREIDLIN-WENTZELL EXIT PROBLEMS [J].

MIKAMI, T .

ANNALS OF PROBABILITY, 1991, 19 (01) :58-82

[24] A large deviation principle for empirical measures on Polish spaces: Application to singular Gibbs measures on manifolds [J].

Garcia-Zelada, David .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2019, 55 (03) :1377-1401

[25] Large Deviations for Empirical Measures of Not Necessarily Irreducible Countable Markov Chains with Arbitrary Initial Measures [J].

Yi Wen Jiang ;

Li Ming Wu .

Acta Mathematica Sinica, 2005, 21 :1377-1390

[26] Large deviations for empirical measures of not necessarily irreducible countable Markov chains with arbitrary initial measures [J].

Jiang, YW ;

Wu, LM .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2005, 21 (06) :1377-1390

[27] Large Deviations for Empirical Measures of Not Necessarily Irreducible Countable Markov Chains with Arbitrary Initial Measures [J].

Yi Wen JIANG Department of MathematicsMilitary Economics AcademyWuhan PRChina Li Ming WU Laborato de Mathmatiques AppliquesCNRS UMR Universit Blaise Paseal AubireFrance and Department MathematicsWuhan UniversityWuhan PRChina .

Acta Mathematica Sinica(English Series), 2005, 21 (06) :1377-1390

[28] Large deviations principle for discrete-time mean-field games [J].

Saldi, Naci .

SYSTEMS & CONTROL LETTERS, 2021, 157

[29] Large deviations for empirical measures of switching diffusion processes with small parameters [J].

Ma, Xiaocui ;

Xi, Fubao .

FRONTIERS OF MATHEMATICS IN CHINA, 2015, 10 (04) :949-963

[30] Large deviations for empirical measures of switching diffusion processes with small parameters [J].

Xiaocui Ma ;

Fubao Xi .

Frontiers of Mathematics in China, 2015, 10 :949-963

← 1 2 3 4 5 →