On the strong convergence of weighted sums of widely dependent random variables. Issue 21 (1st November 2016)

• Record Type: Journal Article
• Authors: Cheng, Dongya; Zhang, Wenhai; Wang, Yuebao
• Is Part Of: Communications in statistics. Volume 45:Issue 21(2016)
• Page Start: 6447
• Page End: 6460
• Publication Date: 2016-11-01
• Subjects: Borel–Cantelli lemma -- Strong convergence -- Weighted sums -- Wide dependence; 60F15; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.922988
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: For widely dependent random variables, we present some results on the strong convergence of weighted sums, including results on almost surely (a.s.) and complete convergence. To this end, we verified some Borel–Cantelli lemmas of the widely dependent random variables. The above-mentioned random variables contain common negatively dependent random variables, some positively dependent random variables, and some others; therefore, the obtained results extend and improve some existing results.