Open Access
November 2005 Rate of convergence in the multidimensional central limit theorem for stationary processes. Application to the Knudsen gas and to the Sinai billiard
Françoise Pène
Ann. Appl. Probab. 15(4): 2331-2392 (November 2005). DOI: 10.1214/105051605000000476
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.

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Copyright © 2005 Institute of Mathematical Statistics
Françoise Pène "Rate of convergence in the multidimensional central limit theorem for stationary processes. Application to the Knudsen gas and to the Sinai billiard," The Annals of Applied Probability 15(4), 2331-2392, (November 2005). https://doi.org/10.1214/105051605000000476
Published: November 2005
Vol.15 • No. 4 • November 2005
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