Applied Mathematics and Optimization, Vol.63, No.3, 385-400, 2011
Necessary Conditions for Optimal Control of Stochastic Evolution Equations in Hilbert Spaces
We consider a nonlinear stochastic optimal control problem associated with a stochastic evolution equation. This equation is driven by a continuous martingale in a separable Hilbert space and an unbounded time-dependent linear operator. We derive a stochastic maximum principle for this optimal control problem. Our results are achieved by using the adjoint backward stochastic partial differential equation.
Keywords:Martingale;Stochastic evolution equation;Stochastic maximum principle;Optimal control;Variational inequality;Adjoint equation;Backward stochastic partial differential equation