  We give an exact solution to the generalized Langevin equation of motion of a
charged Brownian particle in a uniform magnetic field that is driven internally
by an exponentially-correlated stochastic force. A strong dissipation regime is
described in which the ensemble-averaged fluctuations of the velocity exhibit
transient oscillations that arise from memory effects. Also, we calculate
generalized diffusion coefficients describing the transport of these particles
and briefly discuss how they are affected by the magnetic field strength and
correlation time. Our asymptotic results are extended to the general case of
internal driving by correlated Gaussian stochastic forces with finite
autocorrelation times.
