Rate of convergence in the multidimensional central limit theorem for stationary processes.: Application to the Knudsen gas and to the Sinai billiard

• 成果类型: Article
• 署名作者: Pène, F
• 署名单位: Universite de Bretagne Occidentale
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000476
• 发表日期: 2005
• 页码: 2331-2392
• 关键词: 2-dimensional hyperbolic billiards; STATISTICAL PROPERTIES; dispersing billiards; negative curvature; markov partitions; DYNAMICAL-SYSTEMS; geodesic-flow; constant; MANIFOLDS; chains

摘要

We show how Rio's method [Probab. Theory Related Fields 104 (1996) 255-282] can be adapted to establish a rate of convergence in (1)/root n in the multidimensional central limit theorem for some stationary processes in the sense of the Kantorovich metric. We give two applications of this general result: in the case of the Knudsen gas and in the case of the Sinai billiard.