  We present analytic results for the current in a system moving in an
arbitrary periodic potential and driven by weak Gaussian noise with an
arbitrary power spectrum which are valid to order (t_c/t_r)^2, where t_c is the
largest characteristic time of the noise, and t_r is the characteristic
intrawell relaxation time. The dependence of the current on the shape of the
potential, and on the shape of the power spectrum of the noise is illustrated.
It is demonstrated that the direction of the current is opposite when the power
spectrum of the noise has minimum or maximum at zero frequency. A simple
physical mechanism for this behavior is suggested. The behavior of the system
in the limit of slow noise (t_c >>t_r) is also discussed. .
