On some algorithmic and computational problems for neuronal diffusion models

In this work we consider some one-dimensional diffusion processes arising in single neurons' activity modelling and discuss some of the related theoretical and computational first passage time problems. With reference to the Wiener and the Ornstein-Uhlenbeck processes, we outline some theoreticaI methods and algorithmic procedures. In particular, the relevance of the computational methods to infer about asymptotic trends of the firing pdf is pointed ou