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Limiting behavior of the partial sum for negatively superadditive dependent random vectors in Hilbert space. (English) Zbl 1489.60048

Summary: In this paper, We study the complete convergence and \(L_p\)-convergence for the maximum of the partial sum of negatively superadditive dependent random vectors in Hilbert space. The results extend the corresponding ones of M. H. Ko [“Some strong laws of large numbers, \(L_2\)-convergence and complete convergence for \(m\)-AANA random vectors in Hilbert space”, Stochastics (2020; doi:10.1080/17442508.2020.1760867)] to \(H\)-valued negatively superadditive dependent random vectors.

MSC:

60F15 Strong limit theorems
60B11 Probability theory on linear topological spaces
60E05 Probability distributions: general theory
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