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

Abstract

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.