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

Motivated by a typical and well-known problem of neurobiological modeling, a parallel algorithm devised to simulate sample paths of stationary normal processes with rational spectral densities is implemented to evaluate first passage time probability densities for time-varying boundaries. After a self-contained outline of the original problem and of the involved computational framework, the results of numerous simulations are discussed and conclusions are drawn on the effect of a periodic boundary and a Butterworth-type covariance on determining quantitative and qualitative features of first passage time probability densities.