Exponential inequalities for dynamical measures of expanding maps of the interval

被引：24

作者：

Collet, P ^{[1
]}

Martinez, S

Schmitt, B

机构：

[1] Ecole Polytech, CNRS, UMR 7644, Ctr Phys Theor, F-91128 Palaiseau, France

[2] Univ Chile, Fac Ciencias Fis & Matemat, Dept Ingn Matemat, Santiago, Chile

[3] Univ Chile, Ctr Modelamiento Matemat, UMR 2071, Santiago, Chile

[4] Univ Bourgogne, Dept Math, Fac Sci Mirande, F-21004 Dijon, France

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2002年 / 123卷 / 03期

关键词：

empirical measures; Perron-Frobenius operators; decay of correlations;

D O I：

10.1007/s004400200204

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 prove an exponential inequality for the absolutely continuous invariant measure of a piecewise expanding map of the interval. As an immediate corollary we obtain a concentration inequality. We apply these results to the estimation of the rate of convergence of the empirical measure in various metrics and also to the efficiency of the shadowing by sets of positive measure.

引用

页码：301 / 322

页数：22

共 27 条

[1] Iterates of expanding maps
Barbour, AD
Gerrard, RM
Reinert, G
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2000, 116 (02) : 151 - 180
[2] Exponential integrability and transportation cost related to logarithmic sobolev inequalities
Bobkov, SG
Götze, F
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 163 (01) : 1 - 28
[3] Borovkov A.A., 1998, Mathematical Statistics
[4] Specification on the interval
Buzzi, J
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (07) : 2737 - 2754
[5] COLLET P, UNPUB ESTIMATE DECAY
[6] DEVROYE L, 1991, NATO ADV SCI I SER C, P335
[7] ERGODIC PROPERTIES OF INVARIANT-MEASURES FOR PIECEWISE MONOTONIC TRANSFORMATIONS
HOFBAUER, F
KELLER, G
[J]. MATHEMATISCHE ZEITSCHRIFT, 1982, 180 (01) : 119 - 140
[8] PIECEWISE INVERTIBLE DYNAMIC-SYSTEMS
HOFBAUER, F
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1986, 72 (03) : 359 - 386
[9] EXISTENCE OF INVARIANT MEASURES FOR PIECEWISE MONOTONIC TRANSFORMATIONS
LASOTA, A
YORKE, JA
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 186 (459) : 481 - 488
[10] Ledoux M, 1999, LECT NOTES MATH, V1709, P120

← 1 2 3 →