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

WANG Meng-hang, PEI Wen-chen, ZHANG Yu-heng, YING Han-lu, WANG Xue-jun

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

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

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School of Mathematical Sciences, Anhui University

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.

Accepted date: 2017-10-23

Online published: 2020-10-09

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)；

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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

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

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