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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2013, Volume 155, Book 2, Pages 33–43 (Mi uzku1195)  

This article is cited in 3 scientific papers (total in 3 papers)

Estimation of the Rate of Convergence in the Multidimensional Central Limit Theorem for Endomorphisms of Euclidean Space

F. G. Gabbasova, V. T. Dubrovinb

a Kazan State University of Architecture and Engineering
b Kazan (Volga Region) Federal University
Full-text PDF (279 kB) Citations (3)
References:
Abstract: 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.
Received: 24.03.2013
Document Type: Article
UDC: 519.21
Language: Russian
Citation: F. G. Gabbasov, V. T. Dubrovin, “Estimation of the Rate of Convergence in the Multidimensional Central Limit Theorem for Endomorphisms of Euclidean Space”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 155, no. 2, Kazan University, Kazan, 2013, 33–43
Citation in format AMSBIB
\Bibitem{GabDub13}
\by F.~G.~Gabbasov, V.~T.~Dubrovin
\paper Estimation of the Rate of Convergence in the Multidimensional Central Limit Theorem for Endomorphisms of Euclidean Space
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2013
\vol 155
\issue 2
\pages 33--43
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1195}
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  • https://www.mathnet.ru/eng/uzku/v155/i2/p33
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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    References:58
     
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