HAMILTON JACOBI BELLMAN EQUATIONS IN INFINITE DIMENSIONS WITH QUADRATIC AND SUPERQUADRATIC HAMILTONIAN

摘要

We consider Hamilton Jacobi Bellman equations in an infinite di mensional Hilbert space, with quadratic (respectively superquadratic) Hamil tonian and with continuous (respectively lipschitz continuous) final condition. This allows to study stochastic optimal control problems for suitable controlled state equations with unbounded control processes. The results are applied to controlled heat equations.