A NOTE ON EXTREME VALUES OF LOCALLY STATIONARY GAUSSIAN-PROCESSES

We consider the large values of a locally stationary Gaussian process which satisfies Berman's condition on the long-range dependence. The paper discusses the extreme values and the exceedances of a general high boundary by the locally stationary Gaussian processes which are slightly less restricted than Husler, Ann. Probab. 18 (1990), 1141-1158). A general time-transformation implies a useful relation to derive limiting distributions. as for instance of the maximum up to time T as T tends to infinity.