  We study the large-time behaviour of Brownian particles moving through a
viscous medium in a confined potential, and which are further subjected to
position-dependent driving forces that are periodic in time. We focus on the
case where these driving forces are rapidly oscillating with an amplitude that
is not necessarily small. We develop a perturbative method for the
high-frequency regime to find the large-time behavior of periodically driven
stochastic systems. The asymptotic distribution of Brownian particles is then
determined to second order. To first order, these particles are found to
execute small-amplitude oscillations around an effective static potential which
can have interesting forms.
