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

摘要: 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.

Abstract: It is suppose that Xn,n≥1 is a standardized strongly dependent non-stationary Gaussian sequences with data missing,and let rij=EXiXj.The joint limiting distribution of complete and incomplete samples’ maximum is derived as rijln(j-i)→r∈(0,∞).Furthermore,the almost sure convergence of the joint limiting distribution is proved.