END随机变量阵列加权和完全收敛性
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摘要
随机变量加权在实际应用中十分广泛,研究随机变量加权和的收敛性也有着实际的意义。完全收敛性在收敛性质中属于较强的收敛性质,比a.s收敛的收敛性还要强,所以研究加权和的完全收敛性在概率论极限理论中也有一定意义。本文采取对END随机变量进行截尾,利用Rosenthal型最大值不等式得出END随机变量阵列在较弱条件下的完全收敛性。
The weighting of random variables is widely used in practice, and it is of practical significance to study the convergence of weighted sums of random variables. Complete convergence belongs to strong convergence property in convergence property, which is stronger than a.s. convergence and convergence. Therefore, it is of significance to study the complete convergence of weighted sums in probability limit theory. In this paper, the END random variables was truncated and obtained the complete convergence of the END random variable arrays under weaker conditions by using Rosenthal type maximum inequality.
The weighting of random variables is widely used in practice, and it is of practical significance to study the convergence of weighted sums of random variables. Complete convergence belongs to strong convergence property in convergence property, which is stronger than a.s. convergence and convergence. Therefore, it is of significance to study the complete convergence of weighted sums in probability limit theory. In this paper, the END random variables was truncated and obtained the complete convergence of the END random variable arrays under weaker conditions by using Rosenthal type maximum inequality.
引文
[1]HSU P L,ROBBINS H.Complete convergence and the law of large numbers[J].Proc Natl Acad Sci USA,1947,33:25-31.
[2]邱德华,陈平炎.END随机变量序列产生的移动平均过程的收敛性[J].数学物理学报,2015,35A(4):756-768.
[3]郭明乐,袁玉军,祝东进.行为NA随机变量阵列加权和的完全收敛性[J].高校应用数学学报,2013,28(3):266-276.
[4]邱德华.NOD随机变量阵列加权乘积和的完全收敛性[J].高校应用数学学报,2011,26(1):33-40.
[5]郑璐璐,王嫱,王学军.NSD随机变量加权和的强收敛性.[J]中国科学技术大学学报,2015,45(2):101-106.
[6]白志东,苏淳,关于独立和的完全收敛性[J].中国科学(A辑),1985,28:1261-1277.
[7]KUCZMASZEWSKA A,On complete convergence for arrays of rowwise negatively associated random variables[J].Statist Probab Lett,2009,79:116-124.
[8]吴群英,林亮.混合序列的完全收敛性和强收敛性[J].工程数学学报,2004,21(1):75-80.
[9]杨善朝.PA序列部分和的完全收敛性[J].应用概率统计,2001,17(2):197-202.
[10]邵启满,关于ρ-混合序列的完全收敛性[J].数学学报,1989,32(3):377-393.
[11]WANG X H,HU S H.Complete convergence and complete moment convergence for a class of random variables[J].Journal of Inequalities and Applications,2012,229:1-12.
[12]沈爱婷.END变量的若干强极限理论及其应用[D].合肥:安徽大学,2014.
[2]邱德华,陈平炎.END随机变量序列产生的移动平均过程的收敛性[J].数学物理学报,2015,35A(4):756-768.
[3]郭明乐,袁玉军,祝东进.行为NA随机变量阵列加权和的完全收敛性[J].高校应用数学学报,2013,28(3):266-276.
[4]邱德华.NOD随机变量阵列加权乘积和的完全收敛性[J].高校应用数学学报,2011,26(1):33-40.
[5]郑璐璐,王嫱,王学军.NSD随机变量加权和的强收敛性.[J]中国科学技术大学学报,2015,45(2):101-106.
[6]白志东,苏淳,关于独立和的完全收敛性[J].中国科学(A辑),1985,28:1261-1277.
[7]KUCZMASZEWSKA A,On complete convergence for arrays of rowwise negatively associated random variables[J].Statist Probab Lett,2009,79:116-124.
[8]吴群英,林亮.混合序列的完全收敛性和强收敛性[J].工程数学学报,2004,21(1):75-80.
[9]杨善朝.PA序列部分和的完全收敛性[J].应用概率统计,2001,17(2):197-202.
[10]邵启满,关于ρ-混合序列的完全收敛性[J].数学学报,1989,32(3):377-393.
[11]WANG X H,HU S H.Complete convergence and complete moment convergence for a class of random variables[J].Journal of Inequalities and Applications,2012,229:1-12.
[12]沈爱婷.END变量的若干强极限理论及其应用[D].合肥:安徽大学,2014.