LOCAL CENTRAL LIMIT THEOREM AND BERRY-ESSEEN THEOREM FOR SOME NONUNIFORMLY HYPERBOLIC DIFFEOMORPHISMS 被引量：1

LOCAL CENTRAL LIMIT THEOREM AND BERRY-ESSEEN THEOREM FOR SOME NONUNIFORMLY HYPERBOLIC DIFFEOMORPHISMS

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摘要 We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit theorem holds, and the speed in the central limit theorem is O（1/√n）. We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit theorem holds, and the speed in the central limit theorem is O（1/√n）.

作者夏红强

机构地区 College of Sciene

出处《Acta Mathematica Scientia》 SCIE CSCD 2010年第3期701-712,共12页 数学物理学报（B辑英文版）

基金 Supported by NSF of China (10571174) the Scientific Research Foundation of Ministry of Education for Returned Overseas Chinese Scholars the Scientific Research Foundation of Ministry of Human and Resources and Social Security of China for Returned Overseas Scholars

关键词 Local central limit theorem Berry-Esseen theorem nonuniform hyperbolic diffeomorphism Henon map Local central limit theorem Berry-Esseen theorem nonuniform hyperbolic diffeomorphism Henon map

分类号 O175.27 [理学—基础数学]

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1Aaronson J, Denker M. A local limit theorem for stationary processes in the domain of attraction of a normal distribution//Balakrinshnan D, Ibragimov I A, Nevzorov V B, Asymptotic methods in probability and statistics with applications. St. Petersburg: Birkhauser, 2001:215-224.
2Aaronson J, Denker M. Local limit theorems for partial sums of stationary sequences generated by Gibbs- Markov maps. Stoch Dyn, 2001, 1:193-237.
3Benedicks M, Caxleson L. The dynamics of the Henon map. Ann Math, 1991, 133:73-169.
4Breiman L. Probability. Reading: Addison-Wesly, 1968.
5Dunford N, Schwartz J T. Linear operators. Part I. General theory. New York: John Wiley & Sons Inc, 1988.
6Gouezel S. Berry-Esseen theorem and local limit theorem for non-uniformly expanding maps. Annales de I'IHP Probabilites et Statistiques, 2005, 41:997-1024.
7Couezel S. Central limit theorem and stable laws for intermittent maps. Probab Theory and Rel Fields, 2004, 128:82 -122.
8Guivarch Y, Hardy J. Theoremes limites pour une classe de chaines de Markov et applicatios aux diffeomorphisms d'Anosov. Ann Inst H Poincare Probab Statist, 1988, 24:73-98.
9Guivarch Y, Le Jan Y. Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions. Ann scient Ec Norm Sup, 1993 4:23-50.
10Parry W, Potlicott M. Zeta functions and the periodic structure of hyperbolic dynamics. Asterisque, 1990, 187/188:1-268.

引证文献1

1夏红强,檀大耀.A MULTIDIMENSIONAL CENTRAL LIMIT THEOREM WITH SPEED OF CONVERGENCE FOR AXIOM A DIFFEOMORPHISMS[J].Acta Mathematica Scientia,2011,31(3):1123-1132.

1Xiaobo LIU.Quantum Hyperbolic Invariants for Diffeomorphisms of Small Surfaces[J].Acta Mathematica Sinica,English Series,2012,28(4):759-770.
2高振龙.密度核估计的随机中心极限定理[J].山西大学学报（自然科学版）,2010,33(1):43-47.
3张奕.相依样本的U-统计量的Berry-Esseen界限[J].杭州大学学报（自然科学版）,1989,16(4):392-398.
4Yangyou Pan,Xiang Zhang.EMBEDDING FLOWS OF DIFFEOMORPHISMS[J].Annals of Differential Equations,2014,30(2):166-173.
5Hong Qiang XIA.Multidimensional Local Central Limit Theorem of Some Non-uniformly Hyperbolic Systems[J].Acta Mathematica Sinica,English Series,2009,25(4):565-580.
6夏红强,檀大耀.A MULTIDIMENSIONAL CENTRAL LIMIT THEOREM WITH SPEED OF CONVERGENCE FOR AXIOM A DIFFEOMORPHISMS[J].Acta Mathematica Scientia,2011,31(3):1123-1132.
7初仁辛,孙圣和.Digital Spectral Representation of Nonuniformly Sampled Periodic Signals[J].Journal of Harbin Institute of Technology(New Series),1997,4(4):51-54.
8王明锐,靳辉.AN　ANALYTICAL　SOLUTION　OF　HEAT　CONDUCTION　ON　A　LOCALLY　NONUNIFORMLY　HEATED　SURFACE　OF　A　PLATE　WITH　FINITE　THICKNESS[J].Applied Mathematics and Mechanics(English Edition),1996,17(5):487-493.
9NIU Ying-xuan.The central limit theorem and chaos[J].Applied Mathematics(A Journal of Chinese Universities),2009,24(2):230-236.
10Manseob LEE.The Barycenter Property for Robust and Generic Diffeomorphisms[J].Acta Mathematica Sinica,English Series,2016,32(8):975-981.

Acta Mathematica Scientia

2010年第3期

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LOCAL CENTRAL LIMIT THEOREM AND BERRY-ESSEEN THEOREM FOR SOME NONUNIFORMLY HYPERBOLIC DIFFEOMORPHISMS 被引量：1

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