Restricted Ornstein–Uhlenbeck process and applications in neuronal models with periodic input signals

Restricted Gauss–Markov processes are used to construct inhomogeneous leaky integrate-and-fire stochastic models for single neurons activity in the presence of a lower reflecting boundary and periodic input signals. The first-passage time problem through a time-dependent threshold is explicitly developed; numerical, simulation and asymptotic results for firing densities are provided.