{"title":"On Lin's condition for products of random variables with singular joint distribution","authors":"A. Il'inskii, Sofiya Ostrovska","doi":"10.15407/MAG15.01.079","DOIUrl":null,"url":null,"abstract":"The paper presents an elaboration of some results on Lin's conditions. A new proof of the fact that if densities of independent random variables $\\xi_1$ and $\\xi_2$ satisfy Lin's condition, the same is true for their product is presented. Also, it is shown that without the condition of independence, the statement is no longer valid.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15407/MAG15.01.079","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The paper presents an elaboration of some results on Lin's conditions. A new proof of the fact that if densities of independent random variables $\xi_1$ and $\xi_2$ satisfy Lin's condition, the same is true for their product is presented. Also, it is shown that without the condition of independence, the statement is no longer valid.
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