Abstract
Herein we derive the first passage time density (FPTD) for a spike discharge in a single neuron with inputs that produce either inhibitory or excitatory impulses. We study the stochastic dynamics using imbedding approach and derive an integro-differential equation for the FPTD. By taking the kernel in the master equation in separable form, we obtain a third order differential equation. Applying a suitable limiting procedure, we convert the differential equation into that of an O.U. process. Finally we introduce jump-diffusion to study the FPTD of spike train of a single neuron.
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