On the almost sure convergence for sums of negatively superadditive dependent random vectors in Hilbert spaces and its application期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On the almost sure convergence for sums of negatively superadditive dependent random vectors in Hilbert spaces and its application

Authors:	Son Cong Ta Cuong Manh Tran Dung Van Le

Affiliation:	1. Hanoi University of Science, Hanoi, Vietnam;2. congson82@gmail.com;4. The University of Da Nang - University of Science and Education, Da Nang, Vietnam

Abstract:	Abstract This paper develops almost sure convergence for sums of negatively superadditive dependent random vectors in Hilbert spaces, we obtain Chung type SLLN and the Jaite type SLLN for sequences of negatively superadditive dependent random vectors in Hilbert spaces. Rate of convergence is studied through considering almost sure convergence to 0 of tail series. As an application, the almost sure convergence of degenerate von Mises-statistics is investigated.

Keywords:	Almost sure convergence Hilbert spaces negatively superadditive dependent random vectors tail series of random vectors von Mises-statistics