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hal-00139455, version 1

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

Samuel Herrmann () 1, Peter Imkeller

The Annals of Applied Probability 15, 1A (2005) 39-68

  • 1:  Institut Elie Cartan Nancy (IECN)
  • http://www.iecn.u-nancy.fr/
    CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) France

Bibliographic reference

  • Type of document: Articles in peer-reviewed journal
  • Subject: Mathematics/Probability
  • Title: The exit problem for diffusions with time-periodic drift and stochastic resonance.
  • Abstract: 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.
  • Fulltext language: English
  • Journal: The Annals of Applied Probability
  • Audience: international
  • Publication date: 2005
  • Volume: 15
  • Issue: 1A
  • Page, identifiant, ...: 39-68
  • Keyword(s): Stochastic resonance – diffusion – periodic potential – double-well potential – noise-induced transition – exit time distribution – comparison theorem – perturbed dynamical system – spectral theory – low-lying eigenvalue
  • Classification: 60J60 (60H10 86A10)
 
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  • From: Samuel Herrmann <>
  • Submitted on: Friday, 30 March 2007 17:18:21
  • Updated on: Friday, 4 May 2007 11:53:46