《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (1): 5-11.doi: 10.6040/j.issn.1671-9352.0.2018.449
张雅静,陶惠玲,李翔,沈爱婷*
ZHANG Ya-jing, TAO Hui-ling, LI Xiang, SHEN Ai-ting*
摘要： 设{X,Xn,n≥1}是同分布的END(extended negatively dependent)随机变量序列,Sn=∑ni=1Xi, n≥1。研究了完全矩收敛性∑∞n=1nr-2-1/(pq)anE(max1≤k≤n|Sk|1/q-εbn1/(pq))+<∞, ∠ε>0在r>1, q>0, 0
中图分类号:
| [1] HSU P L, ROBBINS H. Complete convergence and the law of large numbers[J]. Proceedings of the National Academy of Sciences, 1947, 33(2):25-31. [2] CHOW Y S. On the rate of moment convergence of sample sums and extremes[J].Bulletin of the Institute of Mathematica Academia Sinica, 1988, 16:177-201. [3] CHEN P Y, WANG D C. Convergence rates for probabilities of moderate deviations for moving average processes[J]. Acta Mathematica Sinica, English Series, 2008, 24(4):611-622. [4] LIANG H Y, LI D L, ROSALSKY A. Complete moment and integral convergence for sums of negatively associated random variables[J]. Acta Mathematica Sinica Eng Sers, 2010, 26(3):419-432. [5] DENG X, WANG X J. Equivalent conditions of complete moment convergence and complete integral convergence for nod sequences[J]. Bulletin of the Korean Mathematical Society, 2017, 54(3):917-933. [6] LIU L. Precise large deviations for dependent random variables with heavy tails[J]. Statistics & Probability Letters, 2009, 79(9):1290-1298. [7] JOAG-DEV K, PROSCHAN F. Negative association of random variables with applications[J]. The Annals of Statistics, 1983, 11(1):286-295. [8] CHEN Y Q, CHEN A Y, NG K W. The strong law of large numbers for extended negatively dependent random variables[J]. Journal of Applied Probability, 2010, 47(4):908-922. [9] SHEN Aiting. Probability inequalities for END sequence and their applications[J]. Journal of Inequalities and Applications, 2011, 2011:1-12. [10] 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. [11] WANG Shijie, WANG Xuejun. Precise large deviations for random sums of END real-valued random variables with consistent variation[J]. Journal of Mathematical Analysis and Applications, 2013, 402(2):660-667. [12] 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]. Journal of the Korean Mathematical Society, 2013, 50(2):379-392. [13] WU Y F, CABRERA M O, VOLODIN A. Complete convergence and complete moment convergence for arrays of rowwise END random variables[J]. Glasnik Matematicki, 2014, 49(2):447-466. [14] WANG X J, ZHENG L L, XU C, et al. Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors[J]. Statistics, 2015, 49(2):396-407. [15] WANG X J, WU Y, HU S H. Exponential probability inequality for m-END random variables and its applications[J]. Metrika, 2016, 79(2):127-147. [16] LIU L. Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails[J]. Science China Mathematics, 2010, 53(6):1421-1434. [17] WU Qunying. Complete convergence for weighted sums of sequences of negatively dependent random variables[J]. Journal of Probability and Statistics, 2011, 2011:1-16. [18] STOUT W F. Almost sure convergence[M]. New York: Academic Press, 1974. |
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