Journées de Probabilités 2007
Optimal stochastic control and BSDEs in infinite dimensions
We present a review of recent results on forward-backward systems of stochastic differential equations in the case where the forward equation is a stochastic evolution equation in a Hilbert space driven by an infinite-dimensional Wiener process. Appropriate formulations are given for an associated semilinear PDE on a Hilbert space, and relationships with optimal control problems of stochastic evolution equations are explained. Applications to optimal control of stochastic partial differential equations are also given.