SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

doi:10.1016/S0252-9602(12)60187-8

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (6): 2388-2400.doi: 10.1016/S0252-9602(12)60187-8

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

甘师信¹|陈平炎²

1.College of Mathematics and Statistics, Wuhan University, Wuhan 430072, China； 2.Department of mathematics, Jinan University, Guangzhou 510630, China

收稿日期:2011-01-03 修回日期:2011-12-06 出版日期:2012-11-20 发布日期:2012-11-20
基金资助:
Supported by the NNSF of China (10671149).

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

GAN Shi-Xin¹, CHEN Ping-Yan²

1.College of Mathematics and Statistics, Wuhan University, Wuhan 430072, China； 2.Department of mathematics, Jinan University, Guangzhou 510630, China

Received:2011-01-03 Revised:2011-12-06 Online:2012-11-20 Published:2012-11-20
Supported by:
Supported by the NNSF of China (10671149).

摘要/Abstract

摘要：

In this paper the authors study the complete, weak and almost sure conver-gence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].

关键词: complete convergence, weak convergence, almost sure convergence, array, weighted sum, NOD random variable sequence

Abstract:

Key words: complete convergence, weak convergence, almost sure convergence, array, weighted sum, NOD random variable sequence

中图分类号:

60F15

甘师信, 陈平炎. SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES[J]. 数学物理学报(英文版), 2012, 32(6): 2388-2400.

GAN Shi-Xin, CHEN Ping-Yan. SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES[J]. Acta mathematica scientia,Series B, 2012, 32(6): 2388-2400.

参考文献

[1] Stout W F. Amolst Sure Convergence. New York: Academic Press, 1974

[2] Thrum R. A remark on almost sure convergence of weighted sums. Probab Theory Rel Fields, 1987, 75: 425–430

[3] Hu T C, Moricz F, Taylor R L. Strong laws of large numbers for arrays of rowwise independent random variables. Acta Math Hung, 1980, 54(1/2): 153–162

[4] Ebrahimi N, Ghosh M. Multivariate negative dependence. Cumm Stat-Theory and Methods, 1981, 10(4): 307–337

[5] Joag-Dev K, Proschan F. Negative association of random variables with applications. Ann Statist, 1983, 11: 286–296

[6] Taylor R L, Patterson, R F, Borzorgnia A. A strong law of large numbers for arrays of rowwise negatively dependent random variables. Stoch Anal Appl, 2002, 20(3): 643–656

[7] Bozorgnia A, Patterson R F, Taylor R L. Limit theorems for dependent random variables//Proc of the First World Congress of Nonlinear Analysts. Berlin, New York: Gruyter Publishers, 1996: 1639–1650

[8] Gan S X, Chen P Y. Strong convergence rate of weighted sums for NOD sequences. Acta Math Sci, 2008, 28A(2): 283–290

[9] Kim T S, Ko M H, Han K H. Strong laws of large numbers for weighted sums of negatively dependent random variables. J Korean Math Soc, 2006, 43(6): 1325–1338

[10] Ko M H, Kim T S. Almost sure convergence for weighted sums of negatively orthant dependent random variables. J Korean Math Soc, 2005, 42(5): 949–957

[11] Ko M H, Han K H, Kim T S. Strong laws of large numbers for weighted sums of negatively dependent random variables. J Korean Math Soc, 2005, 42: 949–957

[12] Wu Y F, Zhu D J. Convergence properties of partial sums for arrays of rowwise negative orthant dependent random variables. J Korean Statist Soc, 2010, 39: 189–197

[13] Hsu P L, Robbins H. Complete convergence and the law of large numbers. Proc Nat Acad Sci, 1947, 33: 25–31

[14] Wu Q Y. Convergence for weighted sums of ˜-mixing random sequences. Math Appl (Chinese), 2002, 15(1): 1–4

[15] Qiu D H, Gan S X. Convergence for weighted sums of ˜-mixing random variables sequences. J of Math (PRC), 2008, 28(3): 258–264

[16] Taylor R L, Hu T C. Strong laws of large numbers for arrays of rowwise independent random elements. Internat J Math Math Sci, 1987, 10(4): 805–817

[17] Chow Y S, Teicher H. Probability Theory. 2nd ed. New York: Springer-Verlag, 1988

[18] Asadian N, Fakoor V, Bozorgnia A. Rosenthal´s type inequalities for negatively orthant dependent random variables. JIRSS, 2006, 5: 69–75

[19] Gan S X. Convergence and laws of large numbers for weighted sums of arrays of Banach valued elements. J Wuhan Univ (Natural Science edition), 1997, 43(5): 569–574

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

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