一类随机变量加权和的完全收敛性

发布时间：2018-09-14 14:55

【摘要】：在本文中,我们主要研究满足Rosenthal型不等式的一类随机变量加权和(?)aniXi的完全收敛性.第一章介绍了研究问题的背景以及加权和在统计及概率两方面的重要应用,重点是在统计方面的现实意义,加权和在概率统计中的广泛应用使得对加权和的研究变得非常重要.第二章介绍了很多相关基本知识,如基本的收敛性,Rosenthal不等式,以及完全收敛性等,又介绍了相关引理及不等式,还包含了一些前人的研究成果,提出了我们的研究方向,为本文的研究打下了良好的基础.第三章讨论了随机变量加权和(?)aniXi在两种条件下的完全收敛性,并做出了一定的推广.本章采用截尾:Markov不等式等方法,在更弱的条件下,研究了满足Rosenthal不等式的一类随机变量加权和的完全收敛性,所得结果改进和推广了已有文献的一些结果.
[Abstract]:In this paper, we mainly study the complete convergence of the weighted sum (?) aniXi of a class of random variables satisfying the Rosenthal type inequality. In the first chapter, the background of the research and the important applications of weighted sum in statistics and probability are introduced. The emphasis is on the practical significance in statistics. The wide application of weighted sum in probability and statistics makes the study of weighted sum very important. In the second chapter, we introduce a lot of basic knowledge, such as the basic convergence of Rosenthal inequality, complete convergence and so on. We also introduce the relevant Lemma and inequality, and also include some previous research results, and put forward our research direction. It lays a good foundation for the research of this paper. In chapter 3, we discuss the complete convergence of weighted random variables and (?) aniXi under two conditions, and generalize them to a certain extent. In this chapter, the complete convergence of the weighted sum of a class of random variables satisfying the Rosenthal inequality is studied under weaker conditions by means of truncated Rosenthal inequality. The results obtained improve and generalize some of the results in previous literatures.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.4

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