同分布ρ~-混合随机变量序列的矩和重对数律的完全收敛性
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摘要
本文研究了同分布ρ-混合随机变量序列的矩和重对数律的完全收敛性的等价条件.第一章讨论了同分布ρ-混合随机变量序列的矩完全收敛性的等价条件.第二章讨论了同分布ρ-混合序列的重对数律的完全收敛性的等价条件.第三章ρ-混合随机变量的正则部分和的最大值的矩.
This thesis discusses the Complete Moment Convergence and Law of Iterated Logarithm for sequence of Identically Distributed p- -Mixing Random Variables. In the first chapter, the sufficient and necessary conditions of Complete Moment Convergence for sequence of identically distributed p-Mixing Random Variables are obtained. In the second chapter, the sufficient and necessary conditions of Law of Iterated Logarithm of Identically Distributed p- -Mixing Random Variables are attained. And in the last chapter, on Moments of the Maximum of Normed Partial Sums of p-Mixing Random Variables are studied.
This thesis discusses the Complete Moment Convergence and Law of Iterated Logarithm for sequence of Identically Distributed p- -Mixing Random Variables. In the first chapter, the sufficient and necessary conditions of Complete Moment Convergence for sequence of identically distributed p-Mixing Random Variables are obtained. In the second chapter, the sufficient and necessary conditions of Law of Iterated Logarithm of Identically Distributed p- -Mixing Random Variables are attained. And in the last chapter, on Moments of the Maximum of Normed Partial Sums of p-Mixing Random Variables are studied.
引文
[1]Zhang Li-xin,Wang Xiu-yun. Convergence rates in the strong laws of asymptotically negatively Associated random fields[J].Appl.Math.J.Chinese Univ.,1999,14(4):406-416.
[2]Zhang Li-xin.A functional central limit theorem for asymptotically negatively dependent random fields [J].Acta Math.Hungar.,2000,86(3);237-259.
[3]Wang Jiang-feng, Lu Feng-bin.Inequalities of Maximum of Partial Sums and Weak Convergence for a Class of Weak Convergence for a Class of Weak Dependent Randm Variables [J].Acta Mathematica Sinica:English Series,2006,22:693-700.
[4]HsuP.L.,RobbinsH.,Complete convergence and the law of large numbers,Proc. Nat.Acad.Sci.USA.,1947,33:25-31.
[5]Lu C.R.,Lin Z.Y.,Limit theory for mixing dependent randomvariables,Beijing: Science Press,1997.
[6]蔡光辉.ρ-混合序列的重对数律[J].数学学报,2006,49(1)：155-160.
[7]Kolmogorov A.N.,Rozanov G.,On the strong mixing conditions of a stationary Gaussian process,Probab.Theory Appl.,1960,2(2):222-227(in Russian).
[8]Zhang L. X.,Wen J.W.,Convergence rates in the strong laws of asymptotically negatively associated random variables. Appl.Math.J. ofChinese Univ.,1999,V.14(4): 406-416.
[9]Bryc,W.and Smolenski,W., Moment conditions for almost sure convergence of weakly correlated random variables, Proc.Amer. Math.Soc.,1993,119,629C635.
[10]Wang,J.F.and Lu,F.B.,Inequalities of maximum of partial sums and weak convergence for a class of weak dependent random variables.ActaMath.Sin.,2006,22, 693-700.
[11]Zhang L.X.,Wen,J.W.,2001.Strong law for sums of B-valued mixing random fields.Chinese Ann.Math.22(A),205-216(in Chinese).
[12]Wang J.F,On the convergence in the law of iterated Logarithm of p-mixing Sequences.Journal of HangZhou TC.2007,6(4),245-248.
[13]Katz M.L.,The probability in the tail of distribution,Ann.Math.Statist., 1963,34:12-318.
[14]Baum L.E.,Katz M.L.,Convergence rate in the law of large numbers,Trans.Amer. Math.Soc.,1965,120:108-123.
[15]Bai Z.D.,Su C.,On the complete convergence for independent sums,Science in China,Ser.A,1985,5:399-412.
[16]Shao Q.M.,Amoment inequality and its applications,ActaMathematica,Chinese Series,1988,31(6):736-747.
[17]陈平炎,柳向东.同分布ρ混合序列的矩完全收敛性[J].数学学报,2008,51(2)：281-290.
[18]Shao Q.M.,Maximal inequality for partial sums of p-mixing Sequences, Ann.Probab.,1995,23(2):948-965.
[19]Zhang L.X.,Wen J.W.,Strong laws for sums of B-valued mixing random fields,Chinese Ann.Math.,Chinese Series,2001,20(2):205-216.
[10]梁汉营,苏淳.NA序列对数律的收敛性[J].科学通报,1998,43(18)：1919-1925.
[21]蔡光辉,ρ-混合随机变量序列重对数律[J].数学通报,2006,49(1)：155-160.
[22]姜德元.关于ρ-混合序列对数律的收敛速度[J].应用数学,2002,15(3)：32-37.
[23]章茜.ρ-混合序列重对数律的收敛速度[J].杭州师范大学学报,8(2)103-106.
[24]Chen P. Gan S X,On moment of and ,Acta Math Scientia,2003,23(A):573-582.(in Chinese)
[25]Liu J,Gan S X, Chen P, The Hajeck-Renyi inequality for the NA random variables and its application, Statist Probab Lett,1999,43:99-10
[2]Zhang Li-xin.A functional central limit theorem for asymptotically negatively dependent random fields [J].Acta Math.Hungar.,2000,86(3);237-259.
[3]Wang Jiang-feng, Lu Feng-bin.Inequalities of Maximum of Partial Sums and Weak Convergence for a Class of Weak Convergence for a Class of Weak Dependent Randm Variables [J].Acta Mathematica Sinica:English Series,2006,22:693-700.
[4]HsuP.L.,RobbinsH.,Complete convergence and the law of large numbers,Proc. Nat.Acad.Sci.USA.,1947,33:25-31.
[5]Lu C.R.,Lin Z.Y.,Limit theory for mixing dependent randomvariables,Beijing: Science Press,1997.
[6]蔡光辉.ρ-混合序列的重对数律[J].数学学报,2006,49(1)：155-160.
[7]Kolmogorov A.N.,Rozanov G.,On the strong mixing conditions of a stationary Gaussian process,Probab.Theory Appl.,1960,2(2):222-227(in Russian).
[8]Zhang L. X.,Wen J.W.,Convergence rates in the strong laws of asymptotically negatively associated random variables. Appl.Math.J. ofChinese Univ.,1999,V.14(4): 406-416.
[9]Bryc,W.and Smolenski,W., Moment conditions for almost sure convergence of weakly correlated random variables, Proc.Amer. Math.Soc.,1993,119,629C635.
[10]Wang,J.F.and Lu,F.B.,Inequalities of maximum of partial sums and weak convergence for a class of weak dependent random variables.ActaMath.Sin.,2006,22, 693-700.
[11]Zhang L.X.,Wen,J.W.,2001.Strong law for sums of B-valued mixing random fields.Chinese Ann.Math.22(A),205-216(in Chinese).
[12]Wang J.F,On the convergence in the law of iterated Logarithm of p-mixing Sequences.Journal of HangZhou TC.2007,6(4),245-248.
[13]Katz M.L.,The probability in the tail of distribution,Ann.Math.Statist., 1963,34:12-318.
[14]Baum L.E.,Katz M.L.,Convergence rate in the law of large numbers,Trans.Amer. Math.Soc.,1965,120:108-123.
[15]Bai Z.D.,Su C.,On the complete convergence for independent sums,Science in China,Ser.A,1985,5:399-412.
[16]Shao Q.M.,Amoment inequality and its applications,ActaMathematica,Chinese Series,1988,31(6):736-747.
[17]陈平炎,柳向东.同分布ρ混合序列的矩完全收敛性[J].数学学报,2008,51(2)：281-290.
[18]Shao Q.M.,Maximal inequality for partial sums of p-mixing Sequences, Ann.Probab.,1995,23(2):948-965.
[19]Zhang L.X.,Wen J.W.,Strong laws for sums of B-valued mixing random fields,Chinese Ann.Math.,Chinese Series,2001,20(2):205-216.
[10]梁汉营,苏淳.NA序列对数律的收敛性[J].科学通报,1998,43(18)：1919-1925.
[21]蔡光辉,ρ-混合随机变量序列重对数律[J].数学通报,2006,49(1)：155-160.
[22]姜德元.关于ρ-混合序列对数律的收敛速度[J].应用数学,2002,15(3)：32-37.
[23]章茜.ρ-混合序列重对数律的收敛速度[J].杭州师范大学学报,8(2)103-106.
[24]Chen P. Gan S X,On moment of and ,Acta Math Scientia,2003,23(A):573-582.(in Chinese)
[25]Liu J,Gan S X, Chen P, The Hajeck-Renyi inequality for the NA random variables and its application, Statist Probab Lett,1999,43:99-10