  We are concerned with the long time behavior of the stochastic Navier--Stokes
system for compressible fluids in dimension two and three. In this setting, the
part of the phase space occupied by the solution depends sensitively on the
choice of the initial state. Our main results are threefold. (i) The kinetic
energy of a solution is universally and asymptotically bounded, independent of
the initial datum. (ii) Time shifts of a solution with initially controlled
energy are asymptotically compact and generate an entire solution defined for
all $t\in R$. (iii) Every solution with initially controlled energy generates a
stationary solution and even an ergodic stationary solution on the closure of
the convex hull of its $\omega$--limit set.
