Null controllability of an infinite dimensional SDE with state- and control-dependent noise

Abstract

We consider a controlled stochastic linear differential equation with state- and control-dependent noise in a Hilbert space H. We investigate the relation between the null controllability of the equation and the existence of the solution of “singular” Riccati operator equations. Moreover, for a fixed interval of time, the null controllability is characterized in terms of the dual state. Examples of stochastic PDEs are also considered.