中文摘要：

设{Xn;n≥1}是一均值为0、方差有限的正相伴平稳序列.记Sn=sum Xk,Mn from k=1 to n =maxk≤n︱Sk︱,n≥1.证明了在一定条件下,由E︱X1︱p（︱X1︱1/α）〈∞可推出对任意的ε〉0,有sum npα-2-αh from n=1 to ∞ （n）E{Mn-εn1/p}＋〈∞,其中h（n）为一在无穷处的缓变函数,{x}＋=max{x,0}.

英文摘要：

Let {Xn,n≥1} be a strictly stationary sequence of positively associated random variables with mean zero and finite variance.Set Sn=sum Xk,Mn from k=1 to n =maxk≤n︱Sk︱,n≥1,under some conditions,we show that E︱X1︱p（︱X1︱1/α）∞ implies for any ε0, sum npα-2-αh from n=1 to ∞ （n）E{Mn-εn1/p}＋∞,where h（n） is a slowly varying function at infinity and {x}＋=max{x,0}.