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Asymptotic expansions in the CLT containing the last known moment in the main part

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Abstract

This paper proposes new asymptotic expansions in the central limit theorem which permit us to approximate distributions of normalized sums of independent symmetric random variables with explicit estimates of the remainder. These expansions contain the last known moment of the original random variables in their main part.

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Acknowledgements

We are grateful to V.V. Senatov for the attention and support. V.V. Senatov (10.03.1951 — 22.06.2021) made an exceptional contribution to solving several central probability problems [19]. For instance, the accaracy of asymptotic expansions in CLT with explicit evaluation of accuracy that can be proved computationally. Senatovs moment characteristics based on Chebyshev – Hermite polynomials institutes for the construction of these expansions, can be rightfully named as Senatov moments in his memory [16, 20].

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  1. MSU, Moscow, Russia

    V. N. Sobolev & A. E. Condratenko

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  1. V. N. Sobolev
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  2. A. E. Condratenko
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Correspondence to A. E. Condratenko.

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Sobolev, V., Condratenko, A. Asymptotic expansions in the CLT containing the last known moment in the main part. J Math Sci 271, 300–309 (2023). https://doi.org/10.1007/s10958-023-06457-3

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