Mutual-information noise benefits in Brownian models of continuous and spiking neurons

The Ito calculus shows that noise benefits can occur in common models of continuous neurons and in random spiking neurons cast as stochastic differential equations. Additive Gaussian noise perturbs the neural dynamical systems as additive Brownian diffusions. The first of two theorems uses a global Lipschitz continuity condition to characterize a stochastic resonance (SR) noise benefit in models of continuous neurons that receive random subthreshold inputs. Brownian diffusions produce an SR noise benefit in the sense that they increase the neuron's mutual information or bit count if the noise mean falls within an interval that depends on model parameters. The second theorem extends an earlier SR result for the random spiking FitzHugh-Nagumo neuron model by replacing a firingrate approximation with exact stochastic dynamics. This gives an interval-based sufficient condition for an SR noise benefit.