{"title":"项为线性 mth 阶自回归序列元素之和的鲍姆-卡茨数列的收敛性","authors":"Maryna Ilienko, Anastasiia Polishchuk","doi":"10.1007/s11253-024-02269-z","DOIUrl":null,"url":null,"abstract":"<p>We establish necessary and sufficient conditions for the convergence of the Baum–Katz series for the sums of elements of linear <i>m</i>th order autoregressive sequences of random variables.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convergence of Baum–Katz Series for Sums Whose Terms are Elements of a Linear mth Order Autoregressive Sequence\",\"authors\":\"Maryna Ilienko, Anastasiia Polishchuk\",\"doi\":\"10.1007/s11253-024-02269-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We establish necessary and sufficient conditions for the convergence of the Baum–Katz series for the sums of elements of linear <i>m</i>th order autoregressive sequences of random variables.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-02-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11253-024-02269-z\",\"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://doi.org/10.1007/s11253-024-02269-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们为线性 m 阶自回归随机变量序列元素之和的 Baum-Katz 序列收敛建立了必要条件和充分条件。
Convergence of Baum–Katz Series for Sums Whose Terms are Elements of a Linear mth Order Autoregressive Sequence
We establish necessary and sufficient conditions for the convergence of the Baum–Katz series for the sums of elements of linear mth order autoregressive sequences of random variables.