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Extending Stochastic Resonance for Neuron Models to General Levy Noise

Summary: Extending Stochastic Resonance for Neuron
Models to General Levy Noise
David Applebaum,
Probability and Statistics Department,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
e-mail: D.Applebaum@sheffield.ac.uk
A recent paper by Patel and Kosko [5] demonstrated stochastic
resonance for general feedback continuous and spiking neuron models
using additive Levy noise constrained to have finite second moments.
In this short paper we drop this constraint and show that their result
extends to general Levy 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. Stochastic resonance then follows by a
"forbidden intervals" theorem as in [5].
Index terms: Levy noise, neuron models, stochastic resonance, sto-
chastic differential equation.


Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield


Collections: Mathematics