Exceedances point processes in the plane of stationary Gaussian sequences with data missing

In this paper, we consider the weak convergence of exceedances point processes in the plane of complete and incomplete stationary Gaussian sequences under some weak dependence conditions. The main results are applied to derive the asymptotic joint distribution of location and height of maximum with data missing, and the joint asymptotic behavior of the location of the first high-level exceedance and the location of the maximum with data missing.