ON MULTIPLE-LEVEL EXCURSIONS BY STATIONARY-PROCESSES WITH DETERMINISTIC PEAKS

A well-known property of stationary Gaussian processes is that the exc ursions over high levels (''peaks'') have a limiting parabolic shape, each determined by a single random parameter. This means, in particula r, that (in the limit) the length of a single excursion above a high l evel determines the length of the (shorter) excursion above each highe r level. In this paper we consider a general class of stationary proce sses with this property. Results of Leadbetter and Hsing (1990) for co nvergence of exceedance random measures are generalized to include mul tiple-level exceedances and developed further for the above class of p rocesses. Specific application is made to stationary normal processes. (C) 1997 Elsevier Science B.V.