We consider the strong solution of a semi linear HJB equation associated with a stochastic optimal control in a Hilbert space H: By strong solution we mean a solution in a L2(μ,H)-Sobolev space setting. Within this framework, the present problem can be treated in a similar fashion to that of a finite-dimensional case. Of independent interest, a related linear problem with unbounded coefficient is studied and an application to the stochastic control of a reaction-diffusion equation will be given.
Analysis | Probability
CHOW P.-L. & MENALDI J.-L., Infinite-dimensional Hamilton-Jacobi-Bellman equations in Gauss-Sobolev spaces, Nonlinear Analysis 29, 415-426 (1997). doi: 10.1016/S0362-546X(96)00043-0