Special Session 80: Theory, numerical methods, and applications of stochastic systems and SDEs/SPDEs
Contents
We present some results on Hamilton Jacobi Bellman equations in an infinite dimensional Hilbert space,
where the Hamiltonian has quadratic and superquadratic growth with
respect to the derivative of the value function, and the coefficients can have polynomial growth with
respect to the state variable. The results allow to study stochastic optimal control problems for suitable
controlled state equations with unbounded control processes. In the case of quadratic hamiltonian, we
show some situations where it is possible to deal with final datum only continuous. The talk is
partially based on a joint work with A. Richou.