Probability density function of leaky integrate-and-fire model with Lévy noise and its numerical approximation

We investigate a numerical analysis of a leaky integrate-and-fire model with Lévy noise. We consider a neuron model in which the probability density function of a neuron in some potential at any time is modeled by a transport equation. Lévy noise is included due to jumps by excitatory and inhibitory impulses. Due to these jumps the resulting equation is a transport equation containing two integrals in the right-hand side (jumps). We design, implement, and analyze numerical methods of finite volume type. Some numerical examples are also included.