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

Son Cong Ta, Cuong Manh Tran and Dung Van Le

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 11, 2770-2786

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.

Date: 2020
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DOI: 10.1080/03610926.2019.1584304

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