  We consider potential type dynamical systems in finite dimensions with two
meta-stable 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 $\epsilon$, and, therefore, are 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, that is, for some optimal intensity $\epsilon (T)$. The
physicists' favorite, measures of quality of periodic tuning--and thus
stochastic resonance--such as spectral power amplification or signal-to-noise
ratio, have proven to be defective. They are not robust w.r.t. effective model
reduction, that is, for the passage to a simplified finite state Markov chain
model reducing the dynamics to a pure jumping between the meta-stable states of
the original system. An entirely probabilistic notion of stochastic resonance
based on the transition dynamics between the domains of attraction of the
meta-stable states--and thus failing to suffer from this robustness defect--was
proposed before in the context of one-dimensional diffusions. It is
investigated for higher-dimensional systems here, by using extensions and
refinements of the Freidlin--Wentzell theory of large deviations for time
homogeneous diffusions. Large deviations principles developed for weakly time
inhomogeneous diffusions 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 meta-stable sets.
