Generalized solutions of HJB equations applied to stochastic control on Hilbert space Original Research Article

In this paper we prove the existence of Borel measurable optimal control laws for infinite-dimensional nonstationary stochastic control problems on Hilbert space. This is based on some recent results on existence of generalized solutions of HJB equations on Hilbert space L2(H,μ), where μ is a suitable reference measure on H. For illustration some examples are presented.