{"title":"具有Rd中值的渐近负相关随机向量的lp收敛、完全收敛和弱大数定律","authors":"Mi-Hwa Ko","doi":"10.1186/s13660-018-1699-6","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, based on the Rosenthal-type inequality for asymptotically negatively associated random vectors with values in <math><msup><mi>R</mi><mi>d</mi></msup></math>, we establish results on <math><msub><mi>L</mi><mi>p</mi></msub></math>-convergence and complete convergence of the maximums of partial sums are established. We also obtain weak laws of large numbers for coordinatewise asymptotically negatively associated random vectors with values in <math><msup><mi>R</mi><mi>d</mi></msup></math>.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"107"},"PeriodicalIF":1.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1699-6","citationCount":"2","resultStr":"{\"title\":\"<ArticleTitle xmlns:ns0=\\\"http://www.w3.org/1998/Math/MathML\\\"><ns0:math><ns0:msub><ns0:mi>L</ns0:mi><ns0:mi>p</ns0:mi></ns0:msub></ns0:math>-convergence, complete convergence, and weak laws of large numbers for asymptotically negatively associated random vectors with values in <ns0:math><ns0:msup><ns0:mi mathvariant=\\\"double-struck\\\">R</ns0:mi><ns0:mi>d</ns0:mi></ns0:msup></ns0:math>\",\"authors\":\"Mi-Hwa Ko\",\"doi\":\"10.1186/s13660-018-1699-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In this paper, based on the Rosenthal-type inequality for asymptotically negatively associated random vectors with values in <math><msup><mi>R</mi><mi>d</mi></msup></math>, we establish results on <math><msub><mi>L</mi><mi>p</mi></msub></math>-convergence and complete convergence of the maximums of partial sums are established. We also obtain weak laws of large numbers for coordinatewise asymptotically negatively associated random vectors with values in <math><msup><mi>R</mi><mi>d</mi></msup></math>.</p>\",\"PeriodicalId\":49163,\"journal\":{\"name\":\"Journal of Inequalities and Applications\",\"volume\":\"2018 1\",\"pages\":\"107\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1186/s13660-018-1699-6\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Inequalities and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13660-018-1699-6\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2018/5/8 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inequalities and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13660-018-1699-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/5/8 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Lp-convergence, complete convergence, and weak laws of large numbers for asymptotically negatively associated random vectors with values in Rd
In this paper, based on the Rosenthal-type inequality for asymptotically negatively associated random vectors with values in , we establish results on -convergence and complete convergence of the maximums of partial sums are established. We also obtain weak laws of large numbers for coordinatewise asymptotically negatively associated random vectors with values in .
期刊介绍：
The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.
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