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On the Strong Laws of Large Numbers for Sequences of Blockwise Pairwise and Coordinatewise Negatively Dependent Random Vectors in Hilbert Spaces

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Abstract

This note establishes the strong laws of large numbers for sequences of blockwise pairwise and coordinatewise negatively dependent random vectors taking values in real separable Hilbert spaces. Extensions of the results in Hien et al. [Appl. Math., 2019] and in Wu and Rosalsky [Glas. Mat. Ser. III, 2015] are given. The sharpness of the results are illustrated by examples/counterexamples.

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ACKNOWLEDGMENTS

The author is grateful to Dr. Le Van Thanh (Vinh University, Vietnam) for his valuable comments.

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  1. Department of Mathematics, Hoa Lu University, Ninh Binh City, Ninh Binh Province, Vietnam

    V. T. N. Anh

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  1. V. T. N. Anh
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Correspondence to V. T. N. Anh.

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(Submitted by A. I. Volodin)

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Anh, V.T. On the Strong Laws of Large Numbers for Sequences of Blockwise Pairwise and Coordinatewise Negatively Dependent Random Vectors in Hilbert Spaces. Lobachevskii J Math 42, 3077–3087 (2021). https://doi.org/10.1134/S1995080222010036

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