Analyzing noisy neuronal dynamics: approximations to integrate-and-fire neuron dynamics with applications to stochastic resonance

The analysis of neuronal responses to noisy input is a daunting task even for severely abstracted model neurons such as the leaky integrate-and-fire neuron. At best, time-consuming numerical methods can be employed, but often results can only be obtained via simulations. This hinders both a deeper understanding of the parameter dependence of the neuronal dynamics under study, and complicates, e.g., fits to experimental data. I will present escape noise approximations to integrate-and-fire neuronal dynamics, which lead to closed form expressions for the interspike-interval density of the neurons response, and discuss applications of these models to noisy neuronal dynamics.