随机向量击中截顶多面体圆锥的概率：大数方面

IF 0.4 Q4 MATHEMATICS

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI:10.1134/s1063454124010102

M. Revyakov

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引用次数: 0

摘要

摘要本文提出了一些条件，在这些条件下，在压缩（自上而下）多面体圆锥，特别是截断圆锥中随机向量的线性组合的命中概率是该线性组合对应向量的舒尔凹函数。要求压缩圆锥是凸的，包含点 0，其边缘平行于坐标轴，并且向量的分布密度是对数凹的符号不变函数。此外，还以微分形式得到了保留大化前序内一个已知前序的函数的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Probability of Random Vector Hitting Truncated Polyhedral Cone: Majorization Aspect

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Probability of Random Vector Hitting Truncated Polyhedral Cone: Majorization Aspect

Abstract

The paper presents conditions under which the probability of hitting a linear combination of random vectors in a compressed (from above) polyhedral cone, in particular, a truncated cone is a Schur-concave function of the vector corresponding to this linear combination. It is required that the compressed cone be convex, contain the point 0, its edges be parallel to the coordinate axes, and the distribution density of the vectors be a logarithmically concave sign-invariant function. In addition, a characterization of functions that preserve one known preorder inside the majorization preorder is obtained in differential form.

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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.