We present a time-dependent level-crossing theory for linear dynamical systems perturbed by colored Gaussian noise. We apply these results to approximate the firing statistics of conductance-based integrate-and-fire neurons receiving excitatory and inhibitory Poissonian inputs. Analytical expressions are obtained for three key quantities characterizing the neuronal response to time-varying inputs: the mean firing rate, the linear response to sinusoidally-modulated inputs, and the pairwise spike-correlation for neurons receiving correlated inputs. The theory yields tractable results that are shown to accurately match numerical simulations, and provides useful tools for the analysis of interconnected neuronal populations.
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