Abstract
In this work, some strong convergence theorems are established for weighted sums of coordinatewise negatively associated random vectors in Hilbert spaces. The results obtained in this paper improve and extend the corresponding ones of Huan et al. (Acta Math. Hung. 144(1):132–149, 2014) as well as correct and improve the corresponding one of Ko (J. Inequal. Appl. 2017:290, 2017).
Highlights
1 Introduction The concept of the complete convergence was first introduced by Hsu and Robbins [3] to prove that the arithmetic mean of independent and identically distributed (i.i.d.) random variables converges completely to the expectation of the random variables
Huan et al [1] introduced the concept of coordinatewise negative association for random vectors in Hilbert space as follows, which is more general than that of Definition 1.2
The results of the complete convergence and the complete moment convergence are established for coordinatewise negatively associated (CNA) random vectors in Hilbert spaces
Summary
The concept of the complete convergence was first introduced by Hsu and Robbins [3] to prove that the arithmetic mean of independent and identically distributed (i.i.d.) random variables converges completely to the expectation of the random variables. Huan et al [1] introduced the concept of coordinatewise negative association for random vectors in Hilbert space as follows, which is more general than that of Definition 1.2. If a sequence of random vectors in Hilbert space is NA, it is CNA.
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