  We study the effect of external stochastic modulation on a system with O(2)
symmetry that exhibits a Hopf or oscillatory instability in the absence of
modulation. The study includes a random component in both the control parameter
of the bifurcation and in the modulation amplitude. Stability boundaries are
computed by either solving the stationary Fokker-Planck equation in the
vicinity of the center manifold of the underlying deterministic system whenever
possible, or by direct numerical solution otherwise. If the modulation
amplitude has a stochastic component, the primary bifurcation is always to
standing waves at a value of the control parameter that depends on the
intensity of the fluctuations. More precisely, and to contrast our results with
the case of a deterministic periodic forcing, the onset of instability in the
standing wave regime is shifted from its deterministic location, and the region
of primary bifurcation to traveling waves disappears yielding instead standing
waves at negative values of the control parameter.
