  The large time dynamics of a periodically driven Fokker-Planck process
possessing several metastable states is investigated. At weak noise transitions
between the metastable states are rare. Their dynamics then represent a
discrete Markovian process characterized by time dependent rates. Apart from
the occupation probabilities, so-called specific probability densities and
localizing functions can be associated to each metastable state. Together,
these three sets of functions uniquely characterize the large time dynamics of
the conditional probability density of the original process. Exact equations of
motion are formulated for these three sets of functions and strategies are
discussed how to solve them. These methods are illustrated and their usefulness
is demonstrated by means of the example of a bistable Brownian oscillator
within a large range of driving frequencies from the slow semiadiabatic to the
fast driving regime.
