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On the Asymptotic Behavior of Probabilities of Moderate Deviations for Combinatorial Sums

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Abstract

In this paper, the asymptotic behavior of probabilities of moderate deviations is investigated for combinatorial sums of independent random variables with moments of order p > 2. The zones are found in which these probabilities are equivalent to the tail of the standard normal law. The width of the zones are expressed in terms of the logarithm of the combinatorial variant of the Lyapunov ratio. Previously, similar results have been obtained by the author under the Bernstein and Linnik conditions. The truncation method is used in proving the new results.

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Funding

This study was carried out with the financial support of the Russian Science Foundation (project no. 23-21-00078).

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  1. St. Petersburg State University, 199034, St. Petersburg, Russia

    A. N. Frolov

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  1. A. N. Frolov
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Correspondence to A. N. Frolov.

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Translated by A. Shishulin

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Frolov, A.N. On the Asymptotic Behavior of Probabilities of Moderate Deviations for Combinatorial Sums. Vestnik St.Petersb. Univ.Math. 56, 559–568 (2023). https://doi.org/10.1134/S1063454123040076

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  • DOI: https://doi.org/10.1134/S1063454123040076

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