Stochastic Maximum Principle for Optimal Control ofPartial Differential   Equations Driven by White Noise
  We prove a stochastic maximum principle ofPontryagin's type for the optimal control of a stochastic partial differential equationdriven by white noise in the case when the set of control actions is convex. Particular attention is paid to well-posedness of the adjoint backward stochastic differential equation and the regularity properties of its solution with values in infinite-dimensional spaces. 
Marco Fuhrman, Ying Hu (IRMAR), Gianmario Tessitore
math.PR math.OC