Complete convergence for sequences of coordinatewise widely orthant dependent random vectors in hilbert spaces

Abstract

In this thesis, we introduce a new dependence concept for a sequence of random vectors taking values in real separable Hilbert spaces called coordinate-wise widely orthant dependence and extend the Baum-Katz Theorem to obtain complete convergence and complete moment convergence for a sequence of co-ordinatewise widely orthant dependent random vectors taking values in Hilbert spaces.