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

被引：0
|
作者：
Frolov, A. N. [1 ]
机构：
[1] St Petersburg State Univ, St Petersburg 199034, Russia
来源：
VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS | 2023年 / 56卷 / 04期
基金：
俄罗斯科学基金会;
关键词：
probabilities of large deviations; probabilities of moderate deviations; combinatorial central limit theorem; combinatorial sums; CENTRAL LIMIT BOUNDS; THEOREMS;
D O I：
10.1134/S1063454123040076
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：559 / 568
页数：10
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