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February 2005 The exit problem for diffusions with time-periodic drift and stochastic resonance
Samuel Herrmann, Peter Imkeller
Ann. Appl. Probab. 15(1A): 39-68 (February 2005). DOI: 10.1214/105051604000000530


Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not robust for the passage to their effective dynamics: continuous-time finite-state Markov chains describing the rough features of transitions between different domains of attraction of metastable points. In the framework of one-dimensional diffusions moving in periodically changing double-well potentials we design a new notion of stochastic resonance which refines Freidlin’s concept of quasi-periodic motion. It is based on exact exponential rates for the transition probabilities between the domains of attraction which are robust with respect to the reduced Markov chains. The quality of periodic tuning is measured by the probability for transition during fixed time windows depending on a time scale parameter. Maximizing it in this parameter produces the stochastic resonance points.


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Samuel Herrmann. Peter Imkeller. "The exit problem for diffusions with time-periodic drift and stochastic resonance." Ann. Appl. Probab. 15 (1A) 39 - 68, February 2005.


Published: February 2005
First available in Project Euclid: 28 January 2005

zbMATH: 1079.60070
MathSciNet: MR2115035
Digital Object Identifier: 10.1214/105051604000000530

Primary: 60H10 , 60J60
Secondary: 34D45 , 60F10 , 60J70 , 86A10

Keywords: Comparison theorem , diffusion , double-well potential , exit time distribution , low-lying eigenvalue , noise-induced transition , periodic potential , perturbed dynamical system , Spectral theory , Stochastic resonance

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.15 • No. 1A • February 2005
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