Applications of Mathematics, Vol. 64, No. 1, pp. 45-59, 2019
On the negative dependence in Hilbert spaces with applications
Nguyen Thi Thanh Hien, Le Van Thanh, Vo Thi Hong Van
Received February 27, 2018. Published online October 1, 2018.
Abstract: This paper introduces the notion of pairwise and coordinatewise negative dependence for random vectors in Hilbert spaces. Besides giving some classical inequalities, almost sure convergence and complete convergence theorems are established. Some limit theorems are extended to pairwise and coordinatewise negatively dependent random vectors taking values in Hilbert spaces. An illustrative example is also provided.
Keywords: negative dependence; pairwise negative dependence; Hilbert space; law of large numbers