A MULTIDIMENSIONAL CENTRAL LIMIT THEOREM WITH SPEED OF CONVERGENCE FOR AXIOM A DIFFEOMORPHISMS  

作　　者：夏红强 檀大耀 

机构地区：[1]College of Science Wuhan Textile University [2]Department of Mathematics and Computer Science Qinzhou University

出　　处：《Acta Mathematica Scientia》2011年第3期1123-1132,共10页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(10571174);the Scientific Research Foundation of Ministry of Education for Returned Overseas Chinese Scholars;Scientific Research Foundation of Ministry of Human Resources and Social Security for Returned Overseas Chinese Scholars

摘　　要：Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ~2：=σ~2 （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ~2 . Moreover, there exists a real number A 〉 0 such that, for any integer n ≥ 1,Π（ m＊（ 1√ nS f n ）,N （0,σ~2 ） ≤A√n, where m＊（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ~2：=σ~2 （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ~2 . Moreover, there exists a real number A 〉 0 such that, for any integer n ≥ 1,Π（ m＊（ 1√ nS f n ）,N （0,σ~2 ） ≤A√n, where m＊（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.

关 键 词：multidimensional central limit theorem Axiom A diffeomorphisms symbolic dynamics transfer operator 

分 类 号：O211.5[理学—概率论与数理统计]