  We consider the model of a single-mode quantum nonlinear oscillator with the
fourth (Kerr) and sixth (over-Kerr) orders of nonlinearity in the presence of
fluctuations of the driving field. We demonstrate that the presence of the
amplitude noise does not significantly affect the multi-photon Rabi transitions
for the Kerr oscillator, and, in contrast, suppresses these oscillations for
the over- Kerr oscillator. We explain the suppression of multi-photon
transitions in the over-Kerr oscillator by quasienergy fluctuations caused by
noise in field amplitude. In contrast, for the Kerr oscillator, these
fluctuations cancel each other for two resonant levels due to the symmetry in
the oscillator quasienergy spectrum.
