Interim Report on Research Supported by Grant AFOSR-82-0187.

This research focused on higher order crossings of time series and their application in spectral analysis, and on the various point processes obtained from stationary processes and their relations to reliability models. The higher order crossings theorem was extended to two dimensions, and the one-dimensional version was used to determine the connection between axis crossings and the frequency content of a stationary process. Considerable progress was made in calculating the asymptotic variance-covariance matrix for the vector of higher-order crossing counts, and time series analysis of highly nonlinear and chaotic stationary processes was carried out. The report summarizes progress in these areas. (Author)