中文摘要：

我们在连续弱并且强烈依赖的静止 Gaussian 过程，在分离时间点取样的这个过程的最大值，和这个过程的部分和的最大值之中学习 asymptotic 关系。如果分离时间点的格子是足够地稀少的，如果格子点是 Pickands 格子或稠密的格子， Gaussian 进程弱依赖、 asymptotically 依赖，这二极端值和和是 asymptotically 独立的，这被显示出如果分离时间点的格子是足够地稀少的。

英文摘要：

We study the asymptotic relation among the maximum of continuous weakly and strongly dependent stationary Gaussian process, the maximum of this process sampled at discrete time points, and the partial sum of this process. It is shown that these two extreme values and the sum are asymptotically independent if the grid of the discrete time points is sufficiently sparse and the Gaussian process is weakly dependent, and asymptotically dependent if the grid points are Pickands grids or dense grids.