Method to calculate the moments of the membrane voltage in a model neuron driven by multiplicative filtered shot noise

Neurons are subject to synaptic inputs from many other cells. These inputs consist of spikes changing the conductivity of the target cell, i.e., they enter the neural dynamics as multiplicative shot noise. Up to now, only for simplified models like current-based (additive-noise) point neurons or models with Gaussian white-noise input, exact solutions are available. We present a method to calculate the exact time-dependent moments for the voltage of a point neuron with conductance-based shot noise and a passive membrane. The exact solutions show features (for instance, maxima of the moments vs time) which are also confirmed by numerical simulations. The theoretical analysis of subthreshold membrane fluctuations may contribute to a better comprehension of neural noise in general. We also discuss how the analytical results may provide additional conditions for estimating parameters from experimental data.