Vectorized simulations of normal processes for first crossing-time problems.

The problem of evaluating first crossing probability densities for stationary normal processes possessing a rational spectral density is approached by means of an effective simulation procedure. We focus our attention on the case of pairs of smooth boundaries, a constant and a periodic one, and on processes possessing two-parameter oscillatory covariances. On the base of the results yielded by our simulations, conclusions are drawn on the effects of the periodic components of covariance and boundaries on shape and features of the first crossing densities.