On complete convergence for weighted sums of coordinatewise negatively associated random vectors in Hilbert spaces

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 const...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2022, 59(4), , pp.879-895
Main Authors: Vu Thi Ngoc Anh, Nguyen Thi Thanh Hien
Format: Article
Language:English
Subjects:
수학
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Summary: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. KCI Citation Count: 0
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.b210509