{"title":"The Kolmogorov Inequality for the Maximum of the Sum of Random Variables and Its Martingale Analogues","authors":"N. E. Kordzakhia, A. A. Novikov, A. N. Shiryaev","doi":"10.1137/s0040585x97t991568","DOIUrl":null,"url":null,"abstract":"We give a survey of the results related to extensions of the Kolmogorov inequality for the distribution of the absolute value of the maximum of the sum of centered independent random variables to the case of martingales considered at random stopping times.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"72 9","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/s0040585x97t991568","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
We give a survey of the results related to extensions of the Kolmogorov inequality for the distribution of the absolute value of the maximum of the sum of centered independent random variables to the case of martingales considered at random stopping times.
期刊介绍：
Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.
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