On complete convergence for weighted sums of coordinatewise widely orthant dependent random vectors in Hilbert spaces

In this article, the concept of coordinatewise widely orthant dependent random vectors is introduced and some results on complete convergence for weighted sums of coordinatewise widely orthant dependent random vectors are established in real separable Hilbert spaces. The results obtained in this article extend the corresponding ones of Wang et al. (2014) from rowwise widely orthant dependent random variables to coordinatewise widely orthant-dependent random vectors and the conclusions stated in Anh and Hien (2022) are also extended from coordinatewise negatively associated random vectors to coordinatewise widely orthant-dependent random vectors.