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

Vu Thi Ngoc Anh|Nguyen Thi Thanh Hien
대한수학회 (The Korean Mathematical Society)|2022.07|대한수학회보 (Bulletin of the KMS)|제59권 제4호|pp. 879-895|DOI 10.4134/BKMS.b210509

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참고문헌

키워드

Hilbert spacestrong law of large numberscomplete convergenceWeighted sumnegative associationslowly varying function
주제분류수학

초록

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.

Abstract

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.

참고문헌 (38)

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