  We obtain necessary and sufficient conditions for equivalence of law for
linear stochastic evolution equations driven by a general Gaussian noise by
identifying the suitable space of controls for the corresponding deterministic
control problem. This result is applied to semilinear (reaction-diffusion)
equations driven by a fractional Brownian motion. We establish the equivalence
of continuous dependence of laws of solutions to semilinear equations on the
initial datum in the topology of pointwise convergence of measures and null
controllability for the corresponding deterministic control problem.
