On the weak laws of large numbers for weighted sums of dependent identically distributed random vectors in Hilbert spaces

2020 ◽  
Author(s):  
Vu T. N. Anh ◽  
Nguyen T. T. Hien
Keyword(s):  
Hilbert Spaces ◽  
Weighted Sums ◽  
Random Vectors ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Weak Laws

scholarly journals Weak Laws of Large Numbers for Negatively Superadditive Dependent Random Vectors in Hilbert Spaces

2021 ◽  
Vol 37 (2) ◽  
Author(s):  
Bui Khanh Hang ◽  
Tran Manh Cuong ◽  
Ta Cong Son
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Separable Hilbert Space ◽  
Weighted Sums ◽  
Random Vectors ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Real Separable Hilbert Space ◽  
Weak Laws ◽  
Random Indices

Let $\{X_{n}, {n}\in \mathbb{N}\}$ be a sequence of negatively superadditive dependent random vectors taking values in a real separable Hilbert space. In this paper, we present the weak laws of large numbers for weighted sums (with or without random indices) of $\{X_{n}, {n}\in \mathbb{N}\}$.

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