Gauss–Markov processes in the presence of a reflecting boundary and applications in neuronal models

Abstract Gauss–Markov processes restricted from below by special reflecting boundaries are considered and the transition probability density functions are determined. Furthermore, the first-passage time density through a time-dependent threshold is studied by using analytical, numerical and asymptotic methods. The restricted Gauss–Markov processes are then used to construct inhomogeneous leaky integrate-and-fire stochastic models for single neurons activity in the presence of a reversal hyperpolarization potential and time-varying input signals.