Necessary and sufficient conditions of optimal control for infinite   dimensional SDEs
  A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes its values in a separable Hilbert space and the control domain need not be convex. The result is obtained by using the adjoint backward stochastic differential equation. 
AbdulRahman Al-Hussein
math.PR