正相伴序列的矩完全收敛性

Complete moment convergence for positively associated sequences

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= Xk,Mn= |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ε0,有 npα-2-αh(n)EMn-εn(1/p)+∞,其中h(n)为一在无穷处的缓变函数,x+=maxx,0.

Abstract: Let Xn,n≥1 be a strictly stationary sequence of positively associated random variables with mean zero and finite variance.Set Sn= Xk,Mn= |Sk|,n≥1, under some conditions,we show that E|X1|p(|X1(1/α)) ∞ implies for any ε0,  npα-2-αh(n)EMn-εn(1/p)+ ∞, where h(n) is a slowly varying function at infinity and x+=maxx,0.