混合随机阵列加权和的若干收敛性质

在{ank, 1≤k≤kn, n≥1}一致可积的条件
下, 利用〖AKρ~D〗混合、 〖AKφ~D〗混合序列矩不等式和截尾法, 证明了〖AKρ~D〗混
合、 〖AKφ~D〗混合阵列行加权和最大值max〖DD(〗〖〗1≤j≤kn〖DD)〗〖J
B((〗∑〖DD(〗j〖〗k=1〖DD)〗ankXnk-E∑〖DD(〗j〖〗k=1〖DD)〗ank
Xnk〖JB))〗的弱收敛、 Lr收敛和完全收敛性.

Some Convergence Properties for Weighted Sum of Mixing Random Arrays

Using the moment inequality for ρ-mixing sequences,φ-mixing sequences and truncated method,we investigated the weak convergence,the Lr convergence and the complete convergence for weighted sum max1≤j≤kn(j∑k=1ankXnk-Ej∑k=1ankXnk) of ρ-mixing arrays and φ-mixing arrays under the condition of {ank,1≤k≤kn,n≥1}-uniform integrability.The results presented in this paper have extended and improved some results in related literature.