  We have considered the underdamped motion of a Brownian particle in the
presence of a correlated external random force. The force is modeled by an
Ornstein-Uhlenbeck process. We investigate the fluctuations of the work done by
the external force on the Brownian particle in a given time interval in the
steady state. We calculate the large deviation functions as well as the
complete asymptotic form of the probability density function of the performed
work. We also discuss the symmetry properties of the large deviation functions
for this system. Finally we perform numerical simulations and they are in a
very good agreement with the analytic results.
