Jump-diffusion processes as models for neuronal activity.

Aiming at an improvement of the existing neuronal models, we consider a mixed process ensuing from the superposition of continuous diffusions and of Poisson time-distributed sequence of impulses and focus our attention on the moments of the firing time. In particular, we consider three different instances: the large jumps model in which each jump causes the neuron firing, the reset model characterized by jumps towards the resting potential and a more general model where constant amplitude excitatory and inhibitory jumps are superimposed on diffusion. By resorting to analytical arguments and to numerical computations, the main behavioral differences of the considered models are outlined.