Dependence Between Extreme Values of Discrete and Continuous Time Locally Stationary Gaussian Processes

The maximum of a continuous, locally stationary Gaussian process which satisfies Bermans condition on the long range dependence is compared with the maximum of this process sampled at discrete time points. These two extreme values are asymptotically totally dependent if the grid of the discrete time points is sufficiently dense, and asymptotically independent if the the grid points are sparse.AMS 2000 Subject Classification. Primary—60F05, Secondary—60G15