Speaker: Federica Masiero, Milano Bicocca
In this talk we consider stochastic differential equations (SDEs) with delay in the state. It is well known that the Ornstein-Uhlenbeck transition semigroup doesn't have regularizing properties, such as the strong Feller property. So in general, the associated Hamilton-Jacobi-Bellman (HJB) equation cannot be solved by a classical fixed point argument. In this talk we consider SDEs with delay and with a special dependence on the past trajectory, and we show regularizing results for the transition semigroup of such SDEs. We consider controlled SDEs with delay and we solve in mild sense the associated HJB equation as a first step to solve the stochastic controlled problem related.
The talk is based on a joint work (in progress) with G.Tessitore.