scholarly journals L p $L_{p}$ -convergence, complete convergence, and weak laws of large numbers for asymptotically negatively associated random vectors with values in R d $\mathbb{R}^{d}$

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Mi-Hwa Ko
Keyword(s):  
Complete Convergence ◽  
Random Vectors ◽  
Laws Of Large Numbers ◽  
Negatively Associated ◽  
Large Numbers ◽  
Weak Laws

scholarly journals COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF SEQUENCES OF AANA RANDOM VARIABLES

2008 ◽  
Vol 50 (3) ◽  
pp. 351-357 ◽  
Author(s):  
GUANG-HUI CAI ◽  
BAO-CAI GUO
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Rocky Mountain ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Strong Laws ◽  
Large Numbers ◽  
Asymptotically Almost Negatively Associated

AbstractLet Xn, n ≥ 1 be an asymptotically almost negatively associated (AANA) sequence of random variables. Some complete convergence and Marcinkiewicz–Zygmund type strong laws of large numbers for an AANA sequence of random variables are obtained. The results obtained generalize the results of Kim, Ko and Lee (Kim, T. S., Ko, M. H. and Lee, I. H. 2004. On the strong laws for asymptotically almost negatively associated random variables. Rocky Mountain J. of Math. 34, 979–989.).

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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