Discrete and Continuous Time Extremes of Gaussian Processes

摘要

Joint distribution of maxima of a Gaussian stationary process on a continuous time and in uniform grid on the real axis is studied. When the grid is sufficiently sparse, maxima are asymptotically independent. When the grid is sufficiently tight, the maxima asymptotically coincide. In the boundary case which we call Pickands' grid, the limit distribution is non-degenerate. It calculated in terms of a Pickands' type constant.