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.
Publié le : 2005-11-14
Classification:
Multidimensional central limit theorem,
Kantorovich metric,
Prokhorov metric,
rate of convergence,
37D50,
60F05
@article{1133965765,
author = {P\`ene, Fran\c coise},
title = {Rate of convergence in the multidimensional central limit theorem for stationary processes. Application to the Knudsen gas and to the Sinai billiard},
journal = {Ann. Appl. Probab.},
volume = {15},
number = {1A},
year = {2005},
pages = { 2331-2392},
language = {en},
url = {http://dml.mathdoc.fr/item/1133965765}
}
Pène, Françoise. Rate of convergence in the multidimensional central limit theorem for stationary processes. Application to the Knudsen gas and to the Sinai billiard. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp. 2331-2392. http://gdmltest.u-ga.fr/item/1133965765/