Effects of random jumps on a neuronal diffusion model with reversal potential

We consider a process obtained from the superposition of constant size jumps with exponentially distributed inter-events intervals to a diffusion process with state-dependent infinitesimal variance corresponding to a model neuron with intrinsic reversal potential. We study the main firing features of the model considered and we compare it with an analoguous one without reversal potential, to enlighten the role of the intrinsic lower boundary when inhibition dominates and when the jump size becomes relevant.