  The Swift-Hohenberg fluid convection system with both local and nonlocal
nonlinearities under the influence of white noise is studied. The objective is
to understand the difference in the dynamical behavior in both local and
nonlocal cases. It is proved that when sufficiently many of its Fourier modes
are forced, the system has a unique invariant measure, or equivalently, the
dynamics is ergodic. Moreover, it is found that the number of modes to be
stochastically excited for ensuring the ergodicity in the local Swift-Hohenberg
system depends {\em only} on the Rayleigh number (i.e., it does not even depend
on the random term itself), while this number for the nonlocal Swift-Hohenberg
system relies additionally on the bound of the kernel in the nonlocal
interaction (integral) term, and on the random term itself
