  We study a parametrically modulated oscillator that has two stable states of
vibrations at half the modulation frequency $\omega_F$. Fluctuations of the
oscillator lead to interstate switching. A comparatively weak additional field
can strongly affect the switching rates, because it changes the switching
activation energies. The change is linear in the field amplitude. When the
additional field frequency $\omega_d$ is $\omega_F/2$, the field makes the
populations of the vibrational states different thus lifting the states
symmetry. If $\omega_d$ differs from $\omega_F/2$, the field modulates the
state populations at the difference frequency, leading to fluctuation-mediated
wave mixing. For an underdamped oscillator, the change of the activation energy
displays characteristic resonant peaks as a function of frequency.
