The strong convergence properties of weighted sums for a class of dependent random variables

Abstract

Let $\{X_{\mathit{ni}},u_n\le i\le v_n,n\ge 1\}$ be an arrays of rowwise pairwise negatively quadrant dependent (NQD) random variables. In this paper, some novel sufficient conditions of L${}^{\mathrm{P}}$-convergence for $\{X_{\mathit{ni}},u_n\le i\le v_n,n\ge 1\}$ are presented. Compared with some previous results, our results are more general, even under the weaker conditions. In addition, the method applied in this paper is different from some previous papers.

Keywords:

• L${}^{\mathrm{P}}$-convergence
• pairwise NQD random variable
• weighted sums

Disclosure statement

The authors declare that there is no conflict of interest regarding the publication of this paper.

Authors contributions

All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

Additional information

Funding

This work was jointly supported by the National Natural Science Foundation of China (Nos. 61773217, 61374080), the Construct Program of the Key Discipline in Hunan Province, the Key University Science Research Project of Anhui Province (No. KJ2016A705), the Key Program in the Youth Talent Support Plan in Universities of Anhui Province (No. gxyqZD2016317).