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

DOI10.1214/105051605000000476zbMATH Open1097.37030arXivmath/0602501OpenAlexW1975623966MaRDI QIDQ2496493

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Publication date: 10 July 2006

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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 $frac1sqrtn$ 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.

Full work available at URL: https://arxiv.org/abs/math/0602501

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