The precise asymptotics of the complete convergence for moving average processes of m-dependent B-valued elements

Let {. t ; t . Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {aj; j . Z} is a sequence of real numbers satisfying ..j=..|aj|<.. Define a moving average process Xt=..j=..aj+t.j,t.1, and Sn=.nt=1Xt,n.1. In this article, by using the weak convergence theorem of {Snn.;n.1}, we study the precise asymptotics of the complete convergence for the sequence {X t ; t . N}.