Complete moment convergence of weighted sums for arrays of negatively dependent random variables and its applications

ABSTRACT

The authors study the complete moment convergence of weighted sums for arrays of rowwise negatively dependent random variables. The obtained results improve the corresponding results of Baek and Park (2010). Convergence of weighted sums for arrays of negatively dependent random variables and its applications. As an application, the authors obtain the complete moment convergence of linear processes based on pairwise negatively dependent random variables. In addition, the authors point out a gap of the proof in Baek and Park (2010) and raise an open problem.

KEYWORDS:

• Complete moment convergence
• Weighted sums
• Negatively dependent random variables
• Linear processes.

Mathematics Subject Classification:

• 60F15; 60G50

Acknowledgments

The authors are grateful to the referee for carefully reading the manuscript and for providing some comments and suggestions which led to improvements in the article.

Funding

The research of Y. Wu was supported by the Humanities and Social Sciences Foundation for the Youth Scholars of Ministry of Education of China (12YJCZH217), the Natural Science Foundation of Anhui Province (1308085MA03), the Key NSF of Anhui Educational Committe (KJ2014A255), the Key Program in the Young Talent Support Plan in Universities of Anhui Province (gxyqZD2016316) and the Scientific Research Foundation for Talents of Tongling University (2015tlxyrc10).