胡学平

• 1:安庆师范大学数学与计算科学学院

摘要(Abstract)：

本文系统总结了随机序(阵)列若干可积的概念、等价条件和相互关系,并通过举例加以说明。通过引入随机阵列两种可积的定义,在这些可积的条件下,利用概率矩不等式研究了相依随机阵列加权和的强收敛性和L~1收敛性。

关键词(KeyWords)： 相依随机序列;一致可积;强收敛性;L~1收敛

Abstract:

Keywords:

基金项目(Foundation): 安徽省高校自然科学基金(KJ2013A179);; 省级精品资源课程项目(2015gxk045)

作者(Author): 胡学平

DOI: 10.13757/j.cnki.cn34-1328/n.2017.01.007

参考文献(References)：

• [1]PYKE R.ROOT D.On convergence in r-mean of normalized partial sums[J].Ann Math Statist,1968,32(9):379-381.
• [2]LANDERS D.ROGGE L.Laws of large numbers for pairwise independent uniformly integrable random variable[J].Math Nachr,1987,130:189-192.
• [3]CHANDRA T K.Uniform integrability in the Cesàm sence and the weak law of large numbers[J].Sankhya:the Indian Yournal of Statistics,1989,51(A):309-317.
• [4]GUT A.The weak law of large numbers for arrays[J].Statist Probab Lett,1992,14:49-52.
• [5]HONG D H,OH K S.On the weak law of large numbers for arrays[J].Statist Probab Lett,1995,22:55-57.
• [6]ORDONEZ CABRERA M.Convergence of weighted sums of random variables and uniform integrability concerning the weights[J].Collect Math,1994,45(2):121-132.
• [7]ORDONEZ CABRERA M,V0L0DIN A.Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability[J].J Math Anal Appl,2005,305:644-658.
• [8]CHANDRA T K.GOSWAMI A.Cesàro integrability and laws of large numbers I[J].J Theoret Probab,2003,16(3):655-669.
• [9]CHANDRA T K.GOSWAMI A.Cesàro integrability and laws of large numbers II[J].J Theoret Probab,2006,19(4):789-815.
• [10]YUAN D M.JUN A.BAO T.Law of numbers for residual Cesaro integrable sequences under dependence assumptions[J].Statist Probab Lett,2009,79:611-618.
• [11]SUNG S H.Weak law of large numbers for arrays of random variables[J].Statist Probab Lett 1999,42(2):101-105.
• [12]SUNG S H.Weak laws for weighted sums of random variables[J].Bull Korean Math Soc,2004,41(2):275-282.
• [13]SUNG S H,LISAWADI S.VOLODIN A.Weak laws of large numbers for arrays under a condition of uniform integrability[J].J Korean Math Soc,2008,45(1):289-300.
• [14]WU Y F,SONG M Z,WANG C H.Complete moment convergence and mean convergence for arrays of rowwise extend negatively dependent random variables[J/OL].The Scientific World journal,(2014:1-7)[2016-09-20].http://dx.doi.org/10.1155/2014/478612.
• [15]吴群英.混合序列的概率极限理论[M].北京:科学出版社,2005.
• [16]杨善朝.混合序列的矩不等式和非参数估计[J].数学学报,1997,40(2):271-279.
• [17]杨善朝.一类随机变量部分和的矩不等式及其应用[J].科学通报,1998,43(17):1823-1827.