Optimality conditions for stochastic boundary control problems governed by semilinear parabolic equations. (English) Zbl 1245.93146

Summary: We study the boundary control problems for stochastic parabolic equations with Neumann boundary conditions. Imposing super-parabolic conditions, we establish the existence and uniqueness of the solution of state and adjoint equations with non-homogeneous boundary conditions by the Galerkin approximations method. We also find that, in this case, the adjoint equation (BSPDE) has two boundary conditions (one is non-homogeneous, the other is homogeneous). Using these results, we derive necessary optimality conditions for the control systems under convex state constraints by the convex perturbation method.


93E20 Optimal stochastic control
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
49K45 Optimality conditions for problems involving randomness
35K99 Parabolic equations and parabolic systems
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