Calculation of the First Passage Time Distribution for the Noisy Integrate-and-Fire Neuron with Discrete Periodic Input

The first passage time problem is an important but challenging problem in computational neuroscience. The existing algorithms especially the integral equation method for calculating the first passage time distribution of the integrate-and-fire neuron was initially proposed in the case where the noisy synaptic signal is continuous. Since the discrete pulse of action potential is the most basic unit in neural communication, it is necessary to generalize the classic method so that it also can be applicable to the case where a discrete component is contained in the synaptic input. Based on this consideration, in this paper our purpose is to extend the integral equation calculation for the first passage time distribution from the continuous case to a more general case where the coherent component in the synaptic input consists of a continuous component and a discrete one.