  The reduction of a continuous Markov process with multiple metastable states
to a discrete rate process is investigated in the presence of slow time
dependent parameters such as periodic external forces or slowly fluctuating
barrier heights. A quantitative criterion is provided under which condition a
kinetic description with time dependent frozen rates applies. Finally it is
shown how the long time behavior of the underlying continuous process can be
retrieved from the knowledge of the discrete process by means of an appropriate
random decoration of the discrete states. As a particular example of the
presented theory an over-damped bistable Brownian oscillator with periodic
driving is discussed.
