Diffusion Models for the Stochastic Activity of Neurons

Abstract

The activity of a neuron, subjected to an input of many small excitatory and inhibitory pulses, is considered. Diffusion equations for transition probabilities and first passage times are derived. Exact expressions result for the moments of the distribution of intervals between action potentials. The determination of the distribution from the moments is discussed. The theory is applied to a model with proportional decay of the postsynaptic potential and to the equivalent circuit of the membrane. Ways of treating refractory properties are described.