ρ-混合序列的重对数律矩收敛的精确渐近性

doi:10.6040/j.issn.1671-9352.0.2016.249

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (4): 13-20.doi: 10.6040/j.issn.1671-9352.0.2016.249

ρ-混合序列的重对数律矩收敛的精确渐近性

张亚运,吴群英^*

桂林理工大学理学院, 广西桂林 541006

收稿日期:2016-06-03 出版日期:2017-04-20 发布日期:2017-04-11
通讯作者: 吴群英(1961— ),女,博士,教授,研究方向为概率极限理论.E-mail:wqy666@glut.edu.cn E-mail:1477852085@qq.com
作者简介:张亚运(1990— ),男,硕士研究生,研究方向为概率极限理论.E-mail:1477852085@qq.com
基金资助:
国家自然科学基金资助项目(11361019);广西自然科学基金资助项目(2015GXNSFAA139008)

Precise asymptotics in the law of iterated logarithm for the moment convergence of ρ-mixing sequences

ZHANG Ya-yun, WU Qun-ying^*

College of Science, Guilin University of Technology, Guilin 541006, Guangxi, China

Received:2016-06-03 Online:2017-04-20 Published:2017-04-11

摘要/Abstract

摘要： 假设{X_n,n≥1}为一列严平稳ρ-混合随机变量,期望为零,方差有限。设S_n=∑X_i, M_n=max_1≤i≤n|S_i|。利用ρ-混合随机变量的矩不等式和中心极限定理,得到了一类ρ-混合随机变量序列部分和以及部分和的最大值重对数矩收敛的精确渐近性。

关键词: 精确渐近性, 矩收敛, 重对数律, ρ-混合序列

Abstract: Let {X_n, n≥1}be a sequence of strictly stationary of ρ-mixing random variables with zero means and finite variances. Set S_n=∑X_i, M_n=max1≤i≤n|S_i|. Using the moment inequality and the central limit theorem of the ρ-mixing random variables.The precise asymptotics in the law of iterated logarithm for the moment convergence of ρ-mixing random variables of the partial sum and the maximum of the partial sum are obtained.

Key words: moment convergence, ρ-mixing random variables, precise asymptotics, the law of iterated logarithm

中图分类号:

O211

张亚运,吴群英. ρ-混合序列的重对数律矩收敛的精确渐近性[J]. 山东大学学报（理学版）, 2017, 52(4): 13-20.

ZHANG Ya-yun, WU Qun-ying. Precise asymptotics in the law of iterated logarithm for the moment convergence of ρ-mixing sequences[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 13-20.

参考文献

[1] CHOW Y S. On the rate of moment convergence of sample sums and extremes[J]. Bulletin of the Institute of Mathematics Academia Sinica, 1988, 16(3):177-201.
[2] LIU Weidong, LIN Zhengyan. Precise asymptotics for a new kind of complete moment convergence[J]. Statistics and Proba-bility Letters, 2006, 76(16):1787-1799.
[3] JIANG Ye, ZHANG Lixin, PANG Tianxiao. Precise rates in the law of logarithm for the moment convergence of i.i.d. random variables[J]. Journal of Mathematical Analysis and Applications, 2007, 327(1):695-714.
[4] KOLMOGOROV A N, ROZANOV Y A. On strong mixing conditions for stationary Gaussian processes[J]. Theory of Proba-bility and Its Applications, 1960, 5(2):204-208.
[5] PELIGRAD M. Convergence rates of the strong law for stationary mixing sequences[J]. Zeitschrift Fjr Wahrscheinlichkeits-Theorie and Verwandte Gebiete, 1985, 70(2):307-314.
[6] SHAO Qiman. On the complete convergence for ρ-mixing sequence [J]. Acta Mathematica Sinica,1989, 32:377-393.
[7] SHAO Qiman. Maximal inequalities for partial sums of ρ-mixing sequences[J]. Annals of Probability, 1995, 23(2):948-965.
[8] ZHAO Yuexu. Precise rates in complete moment convergence for ρ-mixing sequences[J]. Journal of Mathematical Analysis and Applications, 2008, 339(1):553-565.
[9] XIAO Xiaoyong, YIN Hongwei. Precise asymptotics in the law of iterated logarithm for the first moment convergence of i.i.d. random variables [J]. Statistics and Probability Letters, 2012, 82(8):1590-1596.
[10] 附宗魁,吴群英.ρ-混合序列安全矩收敛的精确渐进性[J]. 湖北大学学报(自然科学版), 2015, 5:431-437. FU Zongkui, WU Qunying. Precise asymptotics in the complete moment convergence for ρ-mixing sequence[J]. Journal of Hubei University(Natural Science), 2015, 5:431-437.
[11] IBRAGIMOV I A. A note on the central limit theorems for dependent random variables[J]. Probab Theory Appl, 1975, 20:134-139.
[12] SHAO Qiman. A remark on the invariance principle for ρ-mixing sequence [J]. Chinese Annals of Mathematics:Series A, 1988, 9:377-393.
[13] BILLINGSLEY P. Convergence of probability measures[M]. New York:Wiley, 1968.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

ρ-混合序列的重对数律矩收敛的精确渐近性

Precise asymptotics in the law of iterated logarithm for the moment convergence of ρ-mixing sequences

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

多维度评价

本文评价

推荐阅读 0

[1]	邓小芹,吴群英. NA序列完全矩收敛的精确渐近性[J]. 山东大学学报（理学版）, 2017, 52(1): 102-110.
[2]	张玉,肖犇琼,许可,沈爱婷. NSD随机变量阵列的完全矩收敛性[J]. 山东大学学报（理学版）, 2016, 51(6): 30-36.
[3]	钱硕歌, 杨文志. END随机变量移动平均过程的完全矩收敛性[J]. 山东大学学报（理学版）, 2015, 50(06): 13-18.
[4]	郑璐璐, 葛梅梅, 刘艳芳, 王学军. φ混合序列的完全矩收敛性[J]. 山东大学学报（理学版）, 2015, 50(04): 14-19.