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 process 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 features are explicitly obtained for special monotonically non-increasing thresholds.