First Passage Time Problem for the Ornstein-Uhlenbeck Neuronal Model

Abstract

In this paper we propose a simple and efficient method for computing accurate estimates (in closed form) of the first passage time density of the Ornstein-Uhlenbeck neuronal model through a fixed boundary (i.e. the interspike statistics of the stochastic leaky integrate-and-fire neuron model). This new approach can also provide very tight upper and lower bounds (in closed form) for the exact first passage time density in a systematic manner. Unlike previous approximate analytical attempts, this novel approximation scheme not only goes beyond the linear response and weak noise limit, but it can also be systematically improved to yield the exact results. Furthermore, it is straightforward to extend our approach to study the more general case of a deterministically modulated boundary. © Springer-Verlag Berlin Heidelberg 2006.