  The research work outlined in the present note highlights the essential role
played by the simulation procedures implemented by us on CINECA supercomputers
to complement the mathematical investigations carried within our group over the
past several years. The ultimate target of our research is the understanding of
certain crucial features of the information processing and transmission by
single neurons embedded in complex networks. More specifically, here we provide
a bird's eye look of some analytical, numerical and simulation results on the
asymptotic behavior of first passage time densities for Gaussian processes,
both of a Markov and of a non-Markov type. Several figures indicate significant
similarities or diversities between computational and simulated results.
