  We show that the dynamical Casimir effect in an optomechanical system can be
achieved under incoherent mechanical pumping. We adopt a fully
quantum-mechanical approach for both the cavity field and the oscillating
mirror. The dynamics is then evaluated using a recently-developed master
equation approach in the dressed picture, including both zero and finite
temperature photonic reservoirs. This analysis shows that the dynamical Casimir
effect can be observed even when the mean value of the mechanical displacement
is zero. This opens up new possibilities for the experimental observation of
this effect. We also calculate cavity emission spectra both in the resonant and
the dispersive regimes, providing useful information on the emission process.
