Simulation methods in neuronal modelling

The interspike distribution can be modelled as the first-passage-time distribution of suitable diffusion processes with biologically meaningful boundaries. Since various mathematical difficulties arise when one attempts to obtain closed form solutions for first-passage-time problems, one can resort to simulation methods in order to study the problem. In this paper we pinpoint possible overestimations connected with simulations of first-passage-times for diffusion processes and propose a suitable simulation technique to determine the moments and the distribution of the firing times. After checking the validity of the proposed method in some instances where numerical evaluations for such quantities are available, we apply the simulation algorithm to model the spiking activity by means of a particular diffusion process constrained by a suitable time varying threshold.