Modeling Refractoriness for Stochastically Driven Single Neurons

A description of the sequence of interspike intervals and of the subsequent firing times for single neurons is performed by means of an instantaneous return pro- cess in the presence of refractoriness. Every interspike interval consists of an absolute refractory period of fixed duration followed by a period of relative refractoriness whose duration is described by the first-passage time of the modeling diffusion process through a generally time-dependent threshold. In the cases of Wiener and Ornstein-Uhlenbeck processes, the interspike probability density functions and some of its statistical fea- tures are explicitly obtained for special monotonically non-increasing thresholds.