Precise asymptotics in complete moment convergence of moving-average processes

In this paper, we discuss moving-average process Xk=∑i=-∞∞ai+kɛi, where {ɛi;-∞1+p/2, then limε↘0ε2(r-p)/(2-p)-1∑n=1∞nr/p-2-1/pE{|Sn|-εn1/p}+=p(2-p)(r-p)(2r-p-2)E|Z|2(r-p)/(2-p),where Z has a normal distribution with mean 0 and variance τ2=σ2(∑i=-∞∞ai)2.