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.

中文翻译：

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关于组合和的适度偏差概率的渐近行为

摘要

本文研究了阶矩p > 2 的独立随机变量的组合和的中等偏差概率的渐近行为。找到了这些概率相当于标准正态律尾部的区域。区域的宽度以李亚普诺夫比的组合变体的对数表示。此前，作者在伯恩斯坦和林尼克条件下也得到了类似的结果。采用截断法来证明新的结果。