The Strong Convergence Properties for Partial Sums of m-NA Random Variables

doi:10.13371/j.cnki.chin.q.j.m.2018.02.008

Chinese Quarterly Journal of Mathematics ›› 2018, Vol. 33 ›› Issue (2): 172-180.doi: 10.13371/j.cnki.chin.q.j.m.2018.02.008

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The Strong Convergence Properties for Partial Sums of m-NA Random Variables

School of Mathematical Sciences, Anhui University

Accepted:2017-10-23 Online:2018-06-30 Published:2020-10-09
About author:PEI Wen-chen(1995-), male, native of Tongling, Anhui, B.S.D., engages in statistics; Corresponding author, WANG Xue-jun(1981-), male, native of Hefei, Anhui, a professor of Anhui Universiry, Ph.D., engages in probability theory and mathematical statistics.
Supported by:
Supported by the Natural Science Foundation of Anhui Province(1508085J06)； the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005)； the Students Innovative Training Project of Anhui University(201610357001)；

Abstract

Abstract: In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial sums of m-NA random variables.In addition, the Khintchine-Kolmogorov convergence theorem and Kolmogorov-type strong law of large numbers for m-NA random variables are also obtained. The results obtained in the paper generalize some corresponding ones for independent random variables and some dependent random variables.

Key words: m-NA random variables, Three series theorem, Strong convergence, Kolmogorov-type strong law of large numbers

CLC Number:

O211

WANG Meng-hang, PEI Wen-chen, ZHANG Yu-heng, YING Han-lu, WANG Xue-jun. The Strong Convergence Properties for Partial Sums of m-NA Random Variables[J]. Chinese Quarterly Journal of Mathematics, 2018, 33(2): 172-180.

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The Strong Convergence Properties for Partial Sums of m-NA Random Variables

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