The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 15, Number 4 (2005), 2331-2392.
Rate of convergence in the multidimensional central limit theorem for stationary processes. Application to the Knudsen gas and to the Sinai billiard
Full-text: Open access
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.
Article information
Source
Ann. Appl. Probab., Volume 15, Number 4 (2005), 2331-2392.
Dates
First available in Project Euclid: 7 December 2005
Permanent link to this document
https://projecteuclid.org/euclid.aoap/1133965765
Digital Object Identifier
doi:10.1214/105051605000000476
Mathematical Reviews number (MathSciNet)
MR2187297
Zentralblatt MATH identifier
1097.37030
Subjects
Primary: 37D50: Hyperbolic systems with singularities (billiards, etc.) 60F05: Central limit and other weak theorems
Keywords
Multidimensional central limit theorem Kantorovich metric Prokhorov metric rate of convergence
Citation
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. 15 (2005), no. 4, 2331--2392. doi:10.1214/105051605000000476. https://projecteuclid.org/euclid.aoap/1133965765
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