Journées de Probabilités 2007
Stochastic optimal control problems in Banach spaces
We consider stochastic optimal control problems related to a stochastic controlled evolution equation in a Banach space E. The control problem is treated in its weak formulation, by mean of the backward stochastic differential equation approach. By this approach, also the Hamilton Jacobi Bellman equation is solved.
Finally, we present some applications, in particular to controlled stochastic heat equations.