Some Asymptotic Decompositions in the Central Limit Theorem in the Multidimensional Case

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.