期刊
IEEE TRANSACTIONS ON NEURAL NETWORKS
卷 19, 期 12, 页码 1993-2008出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNN.2008.2005610
关键词
Levy noise; jump diffusion; mutual information; neuron models; signal detection; stochastic resonance (SR)
Levy noise can help neurons detect faint or subthreshold signals. Levy noise extends standard Brownian noise to many types of impulsive jump-noise processes found in real and model neurons as well as in models of finance and other random phenomena. Two new theorems and the Ito calculus show that 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. These results generalize earlier forbidden interval theorems of neuronal stochastic resonance (SR) or noise-injection benefits. Global and local Lipschitz conditions imply 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 (SDE). Simulation results show that the same noise benefits still occur for some infinite-variance stable Levy noise processes even though the theorems themselves apply only to finite-variance Levy noise. The Appendix proves the two Ito-theoretic lemmas that underlie the new Levy noise-benefit theorems.
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