WOD变量的完全收敛性和完全矩收敛性

发布时间：2018-03-03 07:03

本文选题：WOD随机变量　切入点：完全收敛性　出处：《安徽大学》2017年硕士论文　论文类型：学位论文

【摘要】：目前,关于独立随机变量在概率极限理论中的研究成果己经相对完善,但是在实际情况中,样本或者变量不一定是独立的,所以后继有很多学者提出了相依结构,比如负相协变量(简称NA变量)、负象限相依变量(简称NOD变量)、推广的负象限相依变量(简称END变量)以及宽象限相依变量(简称WOD变量),其中最广泛的相依变量就是WOD变量.当下,有不少学者对其进行研究,并取得许多卓有成效的成果,但并不完善.因此对于WOD变量的进一步深入研究具有一定的理论意义以及研究价值.在本文中,首先利用WOD变量的Rosenthal型最大值矩不等式和随机变量的截尾技术,在一般的条件下建立了WO 变量加权和的完全收敛性与WOD变量加权和的最大值序列的完全收敛性,并且给出数值模拟,验证了其理论结果是确实有效的.而完全矩收敛性是一类比完全收敛性更强的收敛性,因此在建立了WOD的完全收敛性的基础上,进一步研究了WOD序列的完全矩收敛性.所得结果推广了若干相依变量的相应结果.本文所建立的WOD变量的完全收敛性和完全矩收敛性的结果丰富和完善了WO 变量的概率极限理论.
[Abstract]:At present, the research on independent random variables in probability limit theory has been relatively perfect, but in the actual situation, the samples or variables are not necessarily independent, so many scholars have proposed the dependent structure. For example, negative dependent variables (na variables for short), negative quadrant dependent variables (NOD variables for short), generalized negative quadrant dependent variables (END variables) and wide quadrant dependent variables (WOD variables for short) are the most widely dependent variables. A quantity is a WOD variable. Many scholars have studied it, and made many fruitful results, but not perfect. Therefore, the further study of WOD variables has certain theoretical significance and research value. Firstly, by using the Rosenthal type maximum moment inequality of WOD variables and the truncation technique of random variables, the complete convergence of the weighted sum of WO variables and the maximal sequence of weighted sums of WOD variables are established under general conditions. Numerical simulation is given to verify the validity of the theoretical results, and the complete moment convergence is a kind of convergence which is stronger than the complete convergence. Therefore, the complete convergence of WOD is established. In this paper, we further study the complete moment convergence of WOD sequences, and generalize the corresponding results of some dependent variables. The results of complete convergence and complete moment convergence of WOD variables established in this paper enrich and perfect the WO variables. The theory of probability limit.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.4

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