Output Stream of Leaky Integrate-and-Fire Neuron Without Diffusion Approximation

Probability density function (pdf) of output interspike intervals (ISI) as well as mean ISI is found in exact form for leaky integrate-and-fire (LIF) neuron stimulated with Poisson stream. The diffusion approximation is not used. The whole range of possible ISI values is represented as infinite union of disjoint intervals: , where and are defined by the LIF's physical parameters. Exact expression for the obtained pdf is different on different intervals and is given as finite sum of multiple integrals. For the first three intervals the integrals are taken which brings about exact expressions with polylogarithm functions. The found distribution can be bimodal for some values of parameters. Conditions, which ensure bimodality are briefly analyzed.