Levy Noise Benefits in Neural Signal Detection

We use the Ito calculus to prove that a general type of white Levy noise will benefit subthreshold neuronal signal detection if the noise process´s scaled drift velocity falls inside an interval that depends on the threshold values. Levy noise generalizes Brownian motion and includes several important jump and impulsive random processes often found in neural and financial-engineering models. A global Lipschitz condition implies that additive white Levy noise can increase the mutual information or bit count of several feedback neuron models that obey a general stochastic differential equation. Simulation results show that the same ´stochastic resonance´ noise benefit occurs for at least some impulsive or infinite-variance (stable) Levy noise processes.