论组合和的适度偏差概率渐近行为

IF 0.4 Q4 MATHEMATICS Vestnik St Petersburg University-Mathematics Pub Date : 2024-01-24 DOI:10.1134/s1063454123040076

A. N. Frolov

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引用次数: 0

摘要

摘要本文研究了具有 p > 2 阶矩的独立随机变量组合和的中等偏差概率的渐近行为。区域的宽度用李亚普诺夫比率的组合变体对数表示。在此之前，作者在伯恩斯坦条件和林尼克条件下也得到过类似的结果。在证明新结果时使用了截断法。

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

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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来源期刊

Vestnik St Petersburg University-Mathematics MATHEMATICS-

CiteScore

0.70

自引率

50.00%

发文量

期刊介绍： Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.