Moment-generating function of output stream of leaky integrate-and-fire neuron

TL;DR

This paper derives an explicit moment-generating function for the output interspike intervals of a leaky integrate-and-fire neuron model under Poisson input, enabling comprehensive statistical analysis of neuron firing patterns.

Contribution

It introduces a new representation of the output interspike interval distribution and explicitly calculates its moment-generating function, advancing neuron stochastic modeling.

Findings

Derived explicit formulas for moments of all orders.

Validated second and third moments through numerical simulations.

Provided a complete statistical characterization of neuron output activity.

Abstract

The statistics of the output activity of a neuron during its stimulation by the stream of input impulses that forms the stochastic Poisson process is studied. The leaky integrate-and-fire neuron is considered as a neuron model. A new representation of the probability distribution function of the output interspike interval durations is found. Based on it, the moment-generating function of the probability distribution is calculated explicitly. The latter, according to Curtiss theorem, completely determines the distribution itself. In particular, explicit expressions are derived from the moment-generating function for the moments of all orders. The first moment coincides with the one found earlier. Formulas for the second and third moments have been checked numerically by direct modeling of the stochastic dynamics of a neuron with specific physical parameters.