摘要
Let {Xn} be a sequence of i.i.d.r. v. s with mean 0 and variance 1, Sn = ∑i=1nXi- Suppose H(x)>0 (x≥0) is a non-decreasing continuous function such that for some γ>0 and x0>0, x-2-γ(x)(x≥x0) is non-decreasing and x -1logH(x) (x≥x0) is non-increasing. If x-1 logH(x)→0 (x→∞), then Sn - W(n)=o (invH(n)) a.s. (n → ∞) holds if and only if EH(t|X1|)<∞ for all t>0.
Let {Xn} be a sequence of i.i.d.r. v. s with mean 0 and variance 1, Sn = ∑i=1nXi- Suppose H(x)>0 (x≥0) is a non-decreasing continuous function such that for some γ>0 and x0>0, x-2-γ(x)(x≥x0) is non-decreasing and x -1logH(x) (x≥x0) is non-increasing. If x-1 logH(x)→0 (x→∞), then Sn - W(n)=o (invH(n)) a.s. (n → ∞) holds if and only if EH(t|X1|)<∞ for all t>0.
基金
Project supported by the National Natural Science Foundation of China.
