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

Abstract

We show how Rio's method [Probab. Theory Related Fields 104 (1996) 255--282] can be adapted to establish a rate of convergence in $\frac{1}{\sqrt{n}}$ 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.

Published at http://dx.doi.org/10.1214/105051605000000476 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Multiple decorrelation and rate of convergence in multidimensional limit theorems for the Prokhorov metric

Cited by in corpus (11)

• On mean central limit theorems for stationary sequences
• Functional correlation decay and multivariate normal approximation for non-uniformly expanding maps
• Central limit theorems with a rate of convergence for time-dependent intermittent maps
• Sunklodas' approach to normal approximation for time-dependent dynamical systems
• A note on the finite-dimensional distributions of dispersing billiard processes
• Stein's method for dynamical systems
• Sharp connections between Berry-Esseen characteristics and Edgeworth expansions for stationary processes
• A vector-valued almost sure invariance principle for Sinai billiards with random scatterers
• An Improved Composite Hypothesis Test for Markov Models with Applications in Network Anomaly Detection
• Rates of convergence for minimal distances in the central limit theorem under projective criteria
• A coupling approach to random circle maps expanding on the average