Large and moderate deviations for bounded functions of slowly mixing Markov chains

被引：6

作者：

Dedecker, Jerome ^{[1
]}

Gouezel, Sebastien ^{[2
]}

Merlevede, Florence ^{[3
]}

机构：

[1] Univ Paris 05, Lab MAP5, UMR CNRS 8145, 45 Rue St Peres, F-75270 Paris 06, France

[2] Univ Nantes, Lab Jean Leray, CNRS UMR 6629, 2 Rue Houssiniere, F-44322 Nantes, France

[3] Univ Paris Est Marne La Vallee, LAMA, UMR CNRS 8050, 5 Blvd Descartes, F-77420 Champs Sur Marne, France

来源：

STOCHASTICS AND DYNAMICS | 2018年 / 18卷 / 02期

关键词：

Deviation inequalities; concentration inequalities; Markov chains; CENTRAL-LIMIT-THEOREM; INTERMITTENT MAPS; INEQUALITY; SEQUENCES; SUMS;

D O I：

10.1142/S021949371850017X

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：

We consider Markov chains which are polynomially mixing, in a weak sense expressed in terms of the space of functions on which the mixing speed is controlled. In this context, we prove polynomial large and moderate deviations inequalities. These inequalities can be applied in various natural situations coming from probability theory or dynamical systems. Finally, we discuss examples from these various settings showing that our inequalities are sharp.

引用

页数：38

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