Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications

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• 作者：LiXin Zhang
• 关键词：sub ; linear expectation ; capacity ; Kolmogorov’s inequality ; Rosenthal’s inequality ; negative dependence ; strong laws of large numbers
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：59
• 期：4
• 页码：751-768
• 全文大小：266 KB
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• 作者单位：LiXin Zhang (1)
  
  1. School of Mathematics, Zhejiang University, Hangzhou, 310027, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

Classical Kolmogorov’s and Rosenthal’s inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers. In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng (2008), we introduce the concept of negative dependence of random variables and establish Kolmogorov’s and Rosenthal’s inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations. As an application, we show that Kolmogorov’s strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite.