α-弱相依序列加权和的几乎处处中心极限定理

Almost Sure Central Limit Theorem for Weighted Sums under α-Weak Dependence

设{Xn,n≥1}为一零均值有界的α-弱相依序列,满足∞∑i=1θi<∞;{αni,1≤i≤n,n≥1}为一实值三角阵列;令Sn,k=k∑i=1αniXi,1≤k≤n.利用随机变量加权和的弱收敛定理与Borel-Cantelli引理,在适当的假设条件下,给出了非平稳有界的α-弱相依序列加权和Sn,n的几乎处处中心极限定理.

Let {Xn,n≥1} be a sequence of bounded α-weak dependence random variances with zero means and ∞∑i=1θi∞,and {ani,1≤i≤n,n≥1} be a triangular array of real numbers,and assume that Sn,k=k∑i=1αniXi,1≤k≤n.By the weak convergence theorem of the weighted sums of random variances and via Borel-Cantelli lemma under some suitable conditions,we discussed the almost sure central limit theorem for weighted sums Sn,n of non-stationary bounded α-weak dependence random variances.