  Asymptotical formulas for the photon distribution function of a quantum
oscillator with time-dependent frequency and damping coefficients, interacting
with a thermal reservoir, are derived in the case of a large mean number of
quanta. Different regimes of excitation of an initial thermal state with an
arbitrary temperature are considered. New formulas are used to predict the
statistical properties of the electromagnetic field created in the experiments
on the Dynamical Casimir Effect which are now under preparation.
