Some examples on the role of noise in neuronal modelling problems

We review some of the important instances in neurobiological context where the contribution of noise has been recognized to be particularly relevant focusing on different unexpected features and open problems that arise in this context. We use as a reference model the Leaky Integrate and Fire model for the neuronal membrane potential. The analysis of this simple model allows us to illustrate a set of features related to the presence of noise. Moreover, we focus on the effect of the composition of different types of noise by introducing jump-diffusion processes and we consider also the phenomena of stochastic and of ghost resonance.