{"title":"具有奇异联合分布的随机变量乘积的林条件","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 Also, it is shown that without the condition of independence, the statement is no longer valid.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2017-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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 Also, it is shown that without the condition of independence, the statement is no longer valid.\",\"PeriodicalId\":48996,\"journal\":{\"name\":\"Probability and Mathematical Statistics-Poland\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2017-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability and Mathematical Statistics-Poland\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.15407/MAG15.01.079\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability and Mathematical Statistics-Poland","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15407/MAG15.01.079","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
On Lin's condition for products of random variables with singular joint distribution
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.
期刊介绍：
PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.
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