Simulation methods in neuronal modeling

The interspike distribution can be modelled as the first-passage-time distribution of suitable diffusion processes with biologically meaningful boundaries. 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 of 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.