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 1/√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. © Institute of Mathematical Statistics, 2005.