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

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

2006-02-22

arxiv.org/abs/math/0602501v1

Annals of Applied Probability 2005, Vol. 15, No. 4, 2331-2392

Mathematics

Probability

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

Scientific paper

10.1214/105051605000000476

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.

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