由混合序列生成的线性过程加权和的极限定理

假设线性过程Xt=∑〖DD(〗∞〖〗j=0〖DD)〗ajξt-j, t≥1, 其中{ξt,t∈Z}为一零均值的混合序列, {aj, j≥0}为一实数序列, 满足∑〖DD(〗∞〖〗j=0〖DD)〗j〖JB(|〗aj〖JB)|〗<∞, {ani,1≤i≤n,n≥1}为一实值的三角阵列, 在适当的假设条件下, 利用混合序列的中心极限定理及相应的概率不等式, 证明了由混合序列生成线性过程加权和的极限定理.

Limit Theorem for Weighted Sums of Linear Processes Generated by Mixing Sequences

Let {Xt,t≥1} be a linear process of the form Xt=∑∞ j=0|aj|ξt-j,where {ξt,t∈Z} is a mixing sequence with zero means,{aj,j≥0} is a sequnce of real numbers with ∑∞ j=0j|aj|<∞ and {ani,1≤i≤n,n≥1} is a triangular array of real numbers,then under some suitable conditions,by means of the central limit theory and corresponding probability inequalities of mixing sequence,we have obtained the limit theorem for weighted sums of linear processes generated by mixing sequences.