Complete Convergence for Weighted Sums and Arrays of Rowwise Extended Negatively Dependent Random Variables

Abstract

In this article, we study the complete convergence for weighted sums of extended negatively dependent random variables and row sums of arrays of rowwise extended negatively dependent random variables. We apply two methods to prove the results: the first of is based on exponential bounds and second is based on the generalization of the classical moment inequality for extended negatively dependent random variables.

Keywords:

• Complete convergence
• Extended negatively dependent sequence
• Negatively dependent

Mathematics Subject Classification:

• 60E15
• 60F15

Acknowledgments

The authors are exceptionally grateful to the referee for offering helpful remarks and comments that improved presentation of the paper. The research of Xuejun Wang was partially supported by the research of Xuejun Wang was partially supported by the National Natural Science Foundation of China (Grant Nos. 11201001, 11226207), the Natural Science Foundation of Anhui Province (1208085QA03, 1308085QA03), Applied Teaching Model Curriculum of Anhui Univeristy (XJYYXKC04), Doctoral Research Start-up Funds Projects of Anhui University and the Students Science Research Training Program of Anhui University (KYXL2012007). The research of Shuhe Hu was partially supported by the National Natural Science Foundation of China (Grant No. 11171001). The research of Tien-Chung Hu was partially supported by the National Science Council of Taiwan R.O.C. The research of Andrei Volodin was partially supported by the Natural Sciences and Engineering Research Council of Canada.