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浙江大学学报（理学版）
Journal of Zhejiang University (Science Edition)  2020, Vol. 47 Issue (5): 559-563    DOI: 10.3785/j.issn.1008-9497.2020.05.007
Mathematics and Computer Science     
Limiting properties of moving average processes for END random variable sequence
SONG Mingzhu, SHAO Jing, LIU Caiyun
Institute of Mathematics and Computing,Tongling University, Tongling 244000, Anhui Province,China
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Abstract  In this paper, we investigate the moving average processes, which is generated by extended negatively dependent (END) random variables Sequence. By using the Rademacher-Menshov type inequality of END random variables sequence, the limit properties of moment complete convergence and almost everywhere convergence of the maximal partial sums for moving average processes are obtained. END random variables sequence are widely used dependent sequence, our results extend the corresponding results in previous papers.

Key words： END random variable sequence      moving average processes      complete moment convergence      limiting properties     
Received: 29 November 2018      Published: 25 September 2020
CLC:  O211.4  
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SONG Mingzhu
SHAO Jing
LIU Caiyun
Cite this article:

SONG Mingzhu, SHAO Jing, LIU Caiyun. Limiting properties of moving average processes for END random variable sequence. Journal of Zhejiang University (Science Edition), 2020, 47(5): 559-563.

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https://www.zjujournals.com/sci/EN/Y2020/V47/I5/559


END随机变量序列移动平均过程的极限性质

介绍了由END随机变量序列生成的移动平均过程，利用END随机变量序列的Rademacher-Menshov型不等式，得到了移动平均过程部分和最大值的矩完全收敛性和几乎处处收敛的极限性质。END随机变量序列是范围较广的相依序列，得到的结论是对前人研究工作的推进。

关键词： END随机变量序列,  矩完全收敛性,  极限性质,  移动平移过程 
1 EBRAHIMI N, GHOSH M. Multivariate negative dependence[J]. Communications in Statistics A, 1981,10(4): 307-337.
2 LIU L. Precise large deviations for dependent random variables with heavy tails[J]. Statistics and Probability Letters, 2009,79(9):1290-1298. DOI: 10.1016/j.spl.2009.02.001.
3 JOAG-DEV K, PROSCHAN F. Negative association of random variables with applications[J]. The Annals of Statistics,1983,11(1):286-295. DOI: 10.1214/aos/1176346079.
4 LIU L. Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails[J]. Science in China (Ser A): Mathematics,2010,53(6):1421-1434. DOI: 10.1007/s11425-010-4012-9.
5 CHEN Y Q, CHEN A Y, NG, KAI W. The strong law of large numbers for extend negatively dependent random variables[J]. Journal of Applied Probability,2010,47:908-922. DOI:10.1017/S0021900200007257.
6 SHEN A T. Probability inequalities for END sequence and their applications[J]. Journal of Inequalities and Applications, 2011, Article ID 98, 12 pages. DOI: 10.1186/1029-242X-2011-98.
7 WU Y F, GUAN M. Convergence properties of the partial sums for sequences of END random variables[J]. Journal of the Korean Mathematical Society, 2012, 49(6): 1097-1110. DOI: 10.4134/JKMS.2012.49.6.1097.
8 WANG S J, WANG X J. Precise large deviations for random sums of END real-valued random variables with consistent variation[J]. Journal of Mathematical Analysis and Applications, 2013, 402:660-667. DOI: 10.1016/j.jmaa.2013.02.002.
9 IBRAGIMOV I A. Some limit theorem for stationary processes[J]. Theory of Probability and Its Applications, 1962(7):349-382. DOI: 10.1137/1107036.
10 ROBERT M B, DEHLING H. Large deviations for some weakly dependent random process[J]. Statistics and Probability Letters, 1990(9):397-401. DOI:10.1016/0617-7152(90)90031-2
11 LI D L, RAO M B , WANG X C. Complete convergence of moving average process[J]. Statistics and Probability Letters, 1992(14): 111-114. DOI: 10.1016/0167-7152(92)90073-E.
12 CHEN P Y, WANG D C. Convergence rates for probabilities of moderate deviations for moving average process[J]. Acta Mathematica Scientia(Eng Ser), 2008,24(4):611-622. DOI: 10.1007/s10114-007-6062-7.
13 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[J]. 数学学报, 2004,47(5): 873-884. DOI: cnki:issn:0583-1431.0.2004-05-005. LI Y X, LI J G. Weak convergence for partial sums of moving average processes generated by stochastic process[J]. Acta Mathematica Sinica, 2004,47(5):873-884. DOI: cnki:issn:0583-1431.0.2004-05-005.
14 ZHANG L X. Complete convergence of moving average processes under dependence assumptions[J]. Statistics and Probability Letters, 1996,30:165-170. DOI: 10.1016/0167-7152(95)00215-4.
15 CHEN P Y, HU T C, VOLODIN A. Limiting behaviour of moving average processes under φ-mixing assumption[J]. Statistics and Probability Letters, 2009,75:105-111. DOI: 10.1016/j.spl.2008.07.026.
16 吴群英.混合序列的概率极限理论[M].北京：科学出版社，2006. WU Q Y. Probability Limit Theory for Mixing Sequences[M]. Beijing: Sicence Press, 2006.
17 SHEN A T, YAO M, XIAO B Q. Equivalent conditions of complete convergence and complete moment convergence for END random variables[J]. Chinese Annals of Mathematics(Ser B), 2018, 39(1): 83-96. DOI: 10.1007/s11401-018-1053-9.
18 LI P H , LI X Q, WU K H. Complete convergence of randomly weighted END and its application[J]. Journal of Inequalities and Applications, 2017（1）：182-197. DOI: 10.1186/s13660-017-1457-1.
19 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（A辑）, 2015, 35(4):756-768. DOI: 10.3969/j.issn.1003-3998.2015.04.012. QIU D H, CHEN P Y. Convergence for moving average processes under END set-up[J]. Acta Mathematica Scientia(Ser A), 2015,35(4):756-768. DOI: 10.3969/j.issn.1003-3998.2015.04.012.
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