Bull. Korean Math. Soc. 2022; 59(4): 879-895
Online first article July 31, 2022 Printed July 31, 2022
https://doi.org/10.4134/BKMS.b210509
Copyright © The Korean Mathematical Society.
Vu Thi Ngoc Anh, Nguyen Thi Thanh Hien
Hoa Lu University; Hanoi University of Science and Technology
This paper establishes the {Baum--Katz} type theorem and the {Marcinkiewicz--Zymund} type strong law of large numbers for sequences of coordinatewise negatively associated and identically distributed random vectors $\{X,X_n,n\ge1\}$ taking values in a Hilbert space $H$ with general normalizing constants $b_n=n^{\alpha}\widetilde L(n^{\alpha})$, where $\widetilde L(\cdot)$ is the de Bruijn conjugate of a slowly varying function $L(\cdot).$ The main result extends and unifies many results in the literature. The sharpness of the result is illustrated by two examples.
Keywords: Weighted sum, negative association, Hilbert space, complete convergence, strong law of large numbers, slowly varying function
MSC numbers: 60F15
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