A vectorized simulation procedure for computations of first crossing time densities of normal processes with oscillatory covariances

A vector algorithm is provided for simulating stochastic stationary normal processes possessing rational spectral densities. Such an algorithm has been conceived and implemented to detrmine first-crossing-time (FCT) probability densities and the related statistics for the general case of time varying boundaries. A self-contained description of the problem and the set up of the mathematical and computational framework are given. The results of numerous simulations are discussed and conclusions are drawn on the effect of boundary's oscillations and covariance's of oscillatory components on determining qualitative and quantitative features of FCT densities. An example in which a program in Fortran language is exploited to obtain the statistics of the FCT is finally included.