Geodesic
Estimation of the Rate of Convergence in the Multidimensional Central Limit Theorem for Endomorphisms of Euclidean Space
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 2, pp. 33-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $W$ be such a nonsingular integer square matrix of order $d$ that $|\mathrm{det}\, W|>1$; $f_i(x)$ are real-valued periodic in each argument Lipschitz-continuous functions defined on the unit hypercube in $R^{\, d}$. We consider $m$-dimensional vectors $(f_1(xW^k),\ldots,f_m(xW^k)), $ $k=1,2,\ldots$ and obtain the estimate of order $O(n^{\varepsilon- 1/2})$ (where $\varepsilon$ is an arbitrarily small number) for the distance between the distribution of the normalized sum of these vectors and the normal distribution at all measurable convex sets from $R^m$.
Keywords: endomorphisms, limit theorem, rate of convergence. 
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     title = {Estimation of the {Rate} of {Convergence} in the {Multidimensional} {Central} {Limit} {Theorem} for {Endomorphisms} of {Euclidean} {Space}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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F. G. Gabbasov; V. T. Dubrovin. Estimation of the Rate of Convergence in the Multidimensional Central Limit Theorem for Endomorphisms of Euclidean Space. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 2, pp. 33-43. http://geodesic.mathdoc.fr/item/UZKU_2013_155_2_a2/

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