Deviation and concentration inequalities for dynamical systems with subexponential decay of correlations

被引：3

作者：

Cuny, Christophe ^{[1
]}

Dedecker, Jerome ^{[2
]}

Merlevede, Florence ^{[3
]}

机构：

[1] Univ Brest, LMBA, CNRS, UMR 6205, 6 Ave Victor Le Gorgeu, F-29238 Brest, France

[2] Univ Paris Cite, CNRS, MAP5, UMR 8145, 45 rue St Peres, F-75006 Paris, France

[3] Univ Gustave Eiffel, Univ Paris Est Creteil, LAMA, CNRS,UMR 8050, F-77454 Marne La Vallee, France

来源：

STOCHASTICS AND DYNAMICS | 2023年 / 23卷 / 03期

关键词：

Large deviations; moderate deviations; nonuniformly expanding maps; Young towers; RECURRENCE TIMES; MAXIMA; RATES; SUMS;

D O I：

10.1142/S0219493723500259

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 obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples showing that the obtained upper bounds are essentially optimal.

引用

页数：18

共 11 条

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[2] Moment bounds and concentration inequalities for slowly mixing dynamical systems
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Massah, Mozhdeh
Nicol, Matthew
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PHYSICAL REVIEW E, 2018, 97 (05)
[9] Large deviation principle for dynamical systems coupled with diffusion-transmutation processes
Befekadu, Getachew K.
SYSTEMS & CONTROL LETTERS, 2019, 125 : 9 - 15
[10] Decay of correlations for non-uniformly expanding systems with general return times
Melbourne, Ian
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ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2014, 34 : 893 - 918

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