一类强相依非平稳高斯序列最大值的几乎处处收敛

Almost sure convergence of the maximum for a class of strongly dependent non-stationary Gaussian sequences

设{Xn,n≥1}为存在样本缺失的标准化强相依非平稳高斯序列,其相关系数rij=EXiXj.在rijln(j-i)→r∈(0,∞)的情况下,得到了完整样本的最大值与非完整样本的最大值的联合极限分布,并证明了其几乎处处收敛.

It is suppose that {Xn,n≥1} is a standardized strongly dependent non - stationary Gaussian se-quences with data missing, and let rij -- EXiXj . The joint limiting distribution of complete and incomplete sam-pies＇ maximum is derived as rijln（j-i）→r∈（0,∞） . Furthermore,the almost sure convergence of the jointlimiting distribution is proved.