Diffusion approximation for a multi-input neuron

A generalization of an earlier paper (Capocelli and Ricciardi, 1971), dealing with a diffusion approximation for a neuron subject to one excitatory and one inhibitory Poisson input, is provided by not imposing any restrictions on number and magnitude if synaptic inputs. An equation for the neuron's transition p.d.f. is derived, use of which is made to determine the moments of the membrane potential. It is finally shown that a diffusion approximation is possible and that the resulting diffusion process is characterized by constant infinitesimal variance and linear drift.