Shot noise in the leaky integrate-and-fire neuron

We study the influence of noise on the transmission of temporal information by a leaky integrate-and-fire neuron using the theory of shot noise. The model includes a finite number of synapses and has a membrane potential variance de facto modulated by the input signal. The phenomenon of stochastic resonance in spiking neurons is analytically exhibited using an inhomogeneous Poisson process model of the spike trains, and links with the traditional Ornstein-Uhlenbeck process obtained by a diffusion approximation are given. It is shown that the modulated membrane potential variance inherent to the model gives better signal processing capabilities than the diffusion approximation.