Stabilization of stochastic parabolic equations with boundary-noise and boundary-control

We consider here a state equation of parabolic type on a bounded real interval, with Neumann boundary conditions consisting in the sum of the control and of a white noise in time. We design a simple form, easily numerically implementable feedback law that assures the exponential stability in probability of the a given equilibrium solution. The form of the feedback involves only the eigenfunctions of the linear operator of the linearized equation.