On complete moment convergence for CAANA random vectors in Hilbert spaces

For a sequence {X-n, n >= 1} of coordinatewise asymptotically almost negatively associated random vectors in Hilbert space, we investigate the convergence of E(n=1)(infinity)1/1+alpha! E(max(1 <= k <= n) ||S-k|| - is an element of n(alpha)) + and Sigma(infinity)(n=1)logn/1+alpha E(maxl <= k <= n||S-k|| - is an element of n(alpha))(+), where Sk = Sigma X-k(i=1)i and a(+) = max{a, 0}. This investigation provides the complete moment convergence for the case alpha r = 1. 2018 Elsevier B.V. All rights reserved.