Parallel simulations in FPT problems for Gaussian processes

The main results of our research related to first passage time (FPT) problems for stationary Gaussian processes are synthetically outlined. The vectorized and parallel algorithm, efficiently implemented on CRAY-T3E in FORTRN90-MPI, allows to simulat a large number of sample paths of Gaussian stochastic processes in order to obtain reliable estimates of probability density functions (pdf) of first passage times through pre-assigned boundaries. The class of Gaussian processes characterized by damped oscillatory covariance functions and by Butterworth-type covariances have been extensively analyzed in the presence of constant and/or periodic boundaries. The analysis based on our simulation procedure has been particularly profitable as it has proved to provide an efficient research tool in all cases of interest to us when closed-form results or analytic evaluation were not available. Last but not least, in some cases it has allowed us to conjecture certain general features of FPT densities that successively have been rigorously proved.