END随机变量序列产生的移动平均过程的收敛性

数学物理学报 ›› 2015, Vol. 35 ›› Issue (4): 756-768.

END随机变量序列产生的移动平均过程的收敛性

邱德华¹, 陈平炎²

1 广东财经大学数学与统计学院, 广州 510320;
2 暨南大学数学系, 广州 510630

收稿日期:2014-07-10 修回日期:2015-02-12 出版日期:2015-08-25 发布日期:2015-08-25
作者简介:邱德华, qiudhua@sina.com;陈平炎, tchenpy@jnu.edu.cn
基金资助:
国家自然科学基金(61300204,11271161)资助

large Convergence for Moving Average Processes Under END Set-up

Qiu Dehua¹, Chen Pingyan²

1 School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320;
2 Department of Mathematics, Jinan University, Guangzhou 510630

Received:2014-07-10 Revised:2015-02-12 Online:2015-08-25 Published:2015-08-25

摘要/Abstract

摘要：

设{Y_n,-∞< n< +∞}是双向无穷的END随机变量序列(不必同分布), {a_n,-∞< n< +∞}是绝对可和的实常数序列, 该文利用END列的Rademacher-Menshov型矩不等式, 得到了移动平均过程X_n=a_i Y_i+n,n≥部分和的最大值的完全收敛性和矩完全收敛性. 所得结果推广和改进了已知的相应的一些结果.

关键词: 完全收敛, 矩完全收敛, END随机变量, 移动平均过程

Abstract:

Let {Y_n,-∞< n< +∞} be a doubly infinite sequence of non-identically distributed extended negatively dependent (END) random variables, {a_n,-∞< n< +∞} an absolutely summable sequence of real numbers. Utilizing the Rademacher-Menshov's inequality of END random variables, the complete convergence and complete moment convergence of the maximal partial sums of moving average processes X_n=a_i Y_i+n,n≥ are obtained, the corresponding results in series of previous papers are enriched and extended.

Key words: Complete convergence, Complete moment convergence, END random variable, Moving average process

中图分类号:

O211.4

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, 35(4): 756-768.

Qiu Dehua, Chen Pingyan. large Convergence for Moving Average Processes Under END Set-up[J]. Acta mathematica scientia,Series A, 2015, 35(4): 756-768.

参考文献

[1] Ibragimov I A. Some limit theorem for stationary processes. Theory Probab Appl, 1962, 7: 349-382
[2] Burton R M, Dehling H. Large deviations for some weakly dependent random processes. Statist Probab Lett, 1990, 9: 397-401
[3] Li D L, Rao M B, Wang X C. Complete convergence of moving average processes. Statist Probab Lett, 1992, 14: 111-114
[4] Chen P Y, Wang D C. Convergence rates for probabilities of moderate deviations for moving average processes. Acta Math Sin (Eng Ser), 2008, 24(4): 611-622
[5] 陈平炎, 管总平. 阵列滑动和的强收敛性. 数学物理学报, 2010, 30A(6): 1394-1401
[6] 李云霞, 李坚高. 由随机过程序列产生的滑动平均过程部分和的弱收敛. 数学学报, 2004, 47(5): 873-884
[7] Zhang L. Complete convergence of moving average processes under dependence assumptions. Statist Probab Lett, 1996, 30: 165-170
[8] Chen P Y, Hu T C, Volodin A. Limiting behavior of moving average processes under φ-mixing assumption. Statist Probab Lett, 2009, 79: 105-111
[9] 李炜, 甘师信. 重尾随机变量序列滑动平均和的极限性质. 数学物理学报, 2013, 33A(4): 787-792
[10] Chow Y S. On the rate of moment complete convergence of sample sums and extremes. Bull Inst Math Acad Sin, 1988, 16: 177-201
[11] Li Y X, Zhang L X. Complete moment convergence of moving average processes under dependence assumptions. Statist Probab Lett, 2004, 70: 191-197
[12] Kim T S, Ko M H. Complete moment convergence of moving average processes under dependence assumptions. Statist Probab Lett,2008, 78: 839-846
[13] Zhou X C. Complete moment convergence of moving average processes under φ-mixing assumptions. Statist Probab Lett, 2010, 80: 285-292
[14] Chen P Y, Hu T H, Volodin A. Limiting behaviour of moving average processes under negative association assumption. Theory Probab Math Statist (Teor Imovir ta Matem Statyst), 2007, 77: 154-166
[15] 陈平炎, 李远梅. 鞅差序列滑动和过程的极限结果. 数学物理学报, 2011, 31A(1): 179-187
[16] 张立新, 王江峰. 两两NQD列的完全收敛性的一个注记. 高校应用数学学报A辑, 2004, 19(2): 203-208
[17] Liu L. Precise large deviations for dependent random variables with heavy tails. Statist Probab Lett, 2009, 79(9): 1290-1298
[18] Joag-Dev K, Proschan F. Negative association of random variables with applications. Ann Statist, 1983, 11(1): 286-295
[19] Liu L. Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails. Sci China Ser A, 2010, 53(6): 1421-1434
[20] Shen A T. Probability inequalities for END sequence and their applications. J Inequal Appl, 2011, DOI: 10.1186/1029-242X-2011-98
[21] Qiu D H, Chen P Y, Antonini R G, et al. On the complete convergence for arrays of rowwise extended negatively dependent random variables. J Korean Math Soc, 2013, 50(2): 379-392
[22] Wu Y F, Guan M. Convergence properties of the partial sums for sequences of END random variables. J Korean Math Soc, 2012, 49: 1097-1110
[23] Wang X J, Hu S H, Hu T C. Complete convergence for weighted sums and arrays of rowwise END sequences. Comm Statist Theory Methods, 2013, 42: 2391-2401
[24] Stout W F. Almost Sure Convergence. New York: Academic Press, 1974