{"title":"Probability of Random Vector Hitting Truncated Polyhedral Cone: Majorization Aspect","authors":"M. Revyakov","doi":"10.1134/s1063454124010102","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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 <i>Schur</i>-concave function of the vector corresponding to this linear combination. It is required that the compressed cone be convex, contain the point <b>0</b>, 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.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik St Petersburg University-Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1063454124010102","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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.
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.
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