Discrete and continuous time extremes of Gaussian processes

Joint distribution of maximums of a Gaussian stationary process in 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 maximums 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. © 2005 Springer Science + Business Media, Inc.