  We present a novel path-integral method for the determination of
time-dependent and time-averaged reaction rates in multidimensional,
periodically driven escape problems at weak thermal noise. The so obtained
general expressions are evaluated explicitly for the situation of a
sinusoidally driven, damped particle with inertia moving in a metastable,
piecewise parabolic potential. A comparison with data from Monte-Carlo
simulations yields a very good agreement with our analytic results over a wide
parameter range.
