The exit problem for diffusions with time-periodic drift and stochastic resonance

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dc.creatorHerrmann, Samuel
dc.creatorImkeller, Peter
dc.date2005-03-22
dc.date.accessioned2026-07-07T05:18:13Z
dc.date.available2026-07-07T05:18:13Z
dc.descriptionPhysical 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.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051604000000530 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0503455
dc.identifierhttp://arxiv.org/abs/math/0503455
dc.identifierAnnals of Applied Probability 2005, Vol. 15, No. 1A, 39-68
dc.identifierdoi:10.1214/105051604000000530
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74582
dc.subjectProbability
dc.subject60H10, 60J60 (Primary) 60J70, 86A10, 60F10, 34D45. (Secondary)
dc.titleThe exit problem for diffusions with time-periodic drift and stochastic resonance
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