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jaykov1 science forum beginner
Joined: 08 Jul 2006
Posts: 3

Posted: Sat Jul 08, 2006 11:31 pm Post subject:
Large deviations principles of NonFreidlinWentzell type.



We consider potential type dynamical systems in finite dimensions with two
metastable states. They are subject to two sources of perturbation: a
slow external periodic perturbation of period T and a small Gaussian
random perturbation of intensity s, and therefore mathematically described
as weakly time inhomogeneous diffusion processes. A system is in stochastic
resonance provided the small noisy perturbation is tuned in such a way that
its random trajectories follow the exterior periodic motion in an optimal
fashion, i.e. for some optimal intensity s(T). The physicists’ favorite
measures of quality of periodic tuning – and thus stochastic resonance –
such as spectral power amplification or signaltonoise ratio have proven
to be defective. They are notrobust w.r.t. effective model reduction, i.e.
for the passage to a simplified finite state Markov chain model reducing
the dynamics to a pure jumping between the metastable states of the
original system. An entirely probabilistic notion of stochastic resonance
based on the transition dynamics between the domains of attraction of the
metastable states – and thus failing to su er from this robustness defect
– was proposed before in the context of onedimensional diffusions. It is
investigated for higher dimensional systems here, by using extensions and
refinements of the FreidlinWentzell theory of large deviations for time
homogeneous di usions. Large deviation principles developed forweakly time
inhomogeneous di usions prove to be key tools for a treatment of the
problem of diffusion exit from a domain and thus for the approach of
stochastic resonance via transition probabilities between metastable
sets.
http://www.geocities.com/jaykovf1/Jakov3.pdf 

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