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

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

DOI: 10.4213/tvp2410

 English version: Theory of Probability and its Applications, 2009, 53:2, 256–268

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