Multidimensional central limit theorem for sums of functions of the trajectories of endomorphisms
- Authors: Dubrovin V.T.1, Gabbasov F.G.1, Chebakova V.J.1
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Affiliations:
- Department of System Analysis and Information Technologies
- Issue: Vol 37, No 4 (2016)
- Pages: 409-417
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198012
- DOI: https://doi.org/10.1134/S1995080216040053
- ID: 198012
Cite item
Abstract
We study the rate of convergence in the central limit theorem for vector-valued sequences generated by endomorphisms of a multidimensional torus. In the proved theorem for sums of functions of the trajectories of endomorphisms of s-dimensional Euclidean space it is obtained almost optimal rate of convergence to the normal distribution. In the proof we use “method of successive approximations”, developed by us earlier (see Dubrovin V.T., Moskvin D.A. Theory of Probability & Its Applications, 1980, V. 24, Is. 3, P. 560–571) to prove limit theorems taking into account the rate of convergence for the sums of functions of sequences that satisfy a mixing condition.
About the authors
V. T. Dubrovin
Department of System Analysis and Information Technologies
Email: vchebakova@mail.ru
Russian Federation, Kremlevskaya ul. 18, Kazan, Tatarstan, 420008
F. G. Gabbasov
Department of System Analysis and Information Technologies
Email: vchebakova@mail.ru
Russian Federation, Kremlevskaya ul. 18, Kazan, Tatarstan, 420008
V. Ju. Chebakova
Department of System Analysis and Information Technologies
Author for correspondence.
Email: vchebakova@mail.ru
Russian Federation, Kremlevskaya ul. 18, Kazan, Tatarstan, 420008