Detectable and undetectable input signals for the integrate-and-fire model

We consider the integrate-and-fire model with non-stationary, stochastic inputs and address the following issue: what are the conditions on the input currents that make the input signal undetectable? A novel theoretical approach to tackle the problem for the model with non-stationary inputs is introduced. When the noise strength is independent of the deterministic component of the synaptic input, an expression for the critical input signal is given. If the input signal is weaker than the critical input signal, the neuron ultimately stops firing, i.e. is not able to detect the input signal; otherwise it fires with probability one. Similar results are established for Poisson type inputs where the strength of the noise is proportional to the deterministic component of the synaptic input.