Complete moment convergence of CWOD sequences and moving average processes based on CWOD in Hilbert spaces

Abstract

In this paper, the concept of coordinatewise widely orthant dependent (CWOD) random vectors is introduced. Some results on complete moment convergence of CWOD sequence and the convergence properties of moving average processes based on CWOD are established in real separable Hilbert spaces. In particular, the complete integral convergence and the complete convergence of moving average processes based on CWOD are derived in Theorem 2.3 and Theorem 2.4, both of which guarantee the corresponding complete moment convergence result ( see Theorem 2.5). Theses conclusions are generalizations of [6], [15], [16], [22] and [26].