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 ", 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 "(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,
i.e. 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 discusions. 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 deviation 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.