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Teoriya Veroyatnostei i ee Primeneniya, 2008, Volume 53, Issue 2, Pages 293–306
DOI: https://doi.org/10.4213/tvp2410 (Mi tvp2410) 		 
Some Asymptotic Decompositions in the Central Limit Theorem in the Multidimensional Case

V. V. Senatov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.4213/tvp2410
Abstract: This paper obtains asymptotic decompositions in the central limit theorem in the multidimensional case with explicit estimates of approximation, which they guarantee. Normalized sums of independent identically distributed random variables with finite moments of the fourth and fifth orders are considered. In constructing the decompositions, analogues of the Chebyshev–Hermite polynomials are used.
Keywords: central limit theorem, multidimensional distributions, asymptotic distributions, multidimensional analogues of Chebyshev-Hermite polynomials.
Received: 03.10.2007
English version:
Theory of Probability and its Applications, 2009, Volume 53, Issue 2, Pages 256–268
DOI: https://doi.org/10.1137/S0040585X97983559
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Language: Russian
Citation: V. V. Senatov, “Some Asymptotic Decompositions in the Central Limit Theorem in the Multidimensional Case”, Teor. Veroyatnost. i Primenen., 53:2 (2008), 293–306; Theory Probab. Appl., 53:2 (2009), 256–268
Citation in format AMSBIB
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