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

Gauss-Markov processes restricted from below by special reflecting boundaries are considered and the transition probability density functions are determined. Furthermore, the firstpassage 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 neuron's activity in the presence of a reversal hyperpolarization potential and different input signals. The case of the periodic input signal is explicitly developed and numerical and asymptotic solutions for the firing densities are provided.