  We consider a particle, confined to a moving harmonic potential, under the
influence of friction and external asymmetric Poissonian shot noise (PSN). We
study the fluctuations of the work done to maintain this system in a
nonequilibrium steady state. PSN generalizes the usual Gaussian noise and can
be considered to be a paradigm of external noise, where fluctuation and
dissipation originate from physically independent mechanisms. We consider two
scenarios: (i) the noise is given purely by PSN and (ii) in addition to PSN the
particle is subject to white Gaussian noise. In both cases we derive exact
expressions for the large deviation form of the work distribution, which are
characterized by the time scales of the system. We show that the usual steady
state fluctuation theorem is violated in our model and that in a certain
parameter regime large negative work fluctuations are more likely to occur than
the corresponding positive ones, though the average work is always positive.
