Extending Stochastic Resonance for Neuron Models to General LÉvy Noise

摘要

A recent paper by Patel and Kosko (2008) demonstrated stochastic resonance (SR) for general feedback continuous and spiking neuron models using additive LÉvy noise constrained to have finite second moments. In this brief, we drop this constraint and show that their result extends to general LÉvy noise models. We achieve this by showing that “large jump” discontinuities in the noise can be controlled so as to allow the stochastic model to tend to a deterministic one as the noise dissipates to zero. SR then follows by a “forbidden intervals” theorem as in Patel and Kosko''s paper.