McDiarmid type inequalities for Wasserstein contractive Markov chains

被引：0

作者：

Wang, Neng-Yi ^{[1
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2025年 / 30卷

基金：

中国国家自然科学基金;

关键词：

concentration inequalities; Markov chains; Wasserstein metrics; TRANSPORTATION;

D O I：

10.1214/25-ECP655

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, under a weak and general condition, we establish explicit McDiarmid type concentration inequalities for general functionals of Wasserstein contractive Markov chains. Our approach is different from those commonly used to establish McDiarmid's inequalities. In particular cases, our result recovers some existing concentration inequalities.

引用

页数：14

共 50 条

[1] A quantitative McDiarmid's inequality for geometrically ergodic Markov chains
Havet, Antoine
Lerasle, Matthieu
Moulines, Eric
Vernet, Elodie
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2020, 25
[2] Subgeometric rates of convergence in Wasserstein distance for Markov chains
Durmus, Alain
Fort, Gersende
Moulines, Eric
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2016, 52 (04): : 1799 - 1822
[3] Perturbation theory for Markov chains via Wasserstein distance
Rudolf, Daniel
Schweizer, Nikolaus
BERNOULLI, 2018, 24 (4A) : 2610 - 2639
[4] Subgaussian concentration inequalities for geometrically ergodic Markov chains
Dedecker, Jerome
Gouezel, Sebastien
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2015, 20 : 1 - 12
[5] Nash inequalities for finite Markov chains
Diaconis, P
SaloffCoste, L
JOURNAL OF THEORETICAL PROBABILITY, 1996, 9 (02) : 459 - 510
[6] CONTRACTIVE COUPLING RATES AND CURVATURE LOWER BOUNDS FOR MARKOV CHAINS
Pedrotti, Francesco
ANNALS OF APPLIED PROBABILITY, 2025, 35 (01) : 196 - 250
[7] ON GRADIENT STRUCTURES FOR MARKOV CHAINS AND THE PASSAGE TO WASSERSTEIN GRADIENT FLOWS
Disser, Karoline
Liero, Matthias
NETWORKS AND HETEROGENEOUS MEDIA, 2015, 10 (02) : 233 - 253
[8] Subexponential Concentration Inequalities for Bifurcating Markov Chains
Wang, Neng-Yi
MARKOV PROCESSES AND RELATED FIELDS, 2024, 30 (02) : 263 - 296
[9] LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS
Diaconis, P.
Saloff-Coste, L.
ANNALS OF APPLIED PROBABILITY, 1996, 6 (03) : 695 - 750
[10] Convergence rates for empirical measures of Markov chains in dual and Wasserstein distances?
Riekert, Adrian
STATISTICS & PROBABILITY LETTERS, 2022, 189

← 1 2 3 4 5 →