{"title":"变量幂约束下高斯随机变量中多项式的分布","authors":"E. D. Kosov","doi":"10.1134/S0016266322020034","DOIUrl":null,"url":null,"abstract":"<p> We study the densities of measures that are polynomial images of the standard Gaussian measure on <span>\\(\\mathbb{R}^n\\)</span>. We assume that the degree of a polynomial is fixed and each variable appears in the monomials of the polynomial to powers bounded by another fixed number. </p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Distributions of Polynomials in Gaussian Random Variables under Constraints on the Powers of Variables\",\"authors\":\"E. D. Kosov\",\"doi\":\"10.1134/S0016266322020034\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> We study the densities of measures that are polynomial images of the standard Gaussian measure on <span>\\\\(\\\\mathbb{R}^n\\\\)</span>. We assume that the degree of a polynomial is fixed and each variable appears in the monomials of the polynomial to powers bounded by another fixed number. </p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0016266322020034\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S0016266322020034","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Distributions of Polynomials in Gaussian Random Variables under Constraints on the Powers of Variables
We study the densities of measures that are polynomial images of the standard Gaussian measure on \(\mathbb{R}^n\). We assume that the degree of a polynomial is fixed and each variable appears in the monomials of the polynomial to powers bounded by another fixed number.
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