| Abstract: |
| For a class of stochastic delay evolution equations driven by cylindrical $Q$-Wiener process, we study the Pontryagin`s maximum principle for the stochastic recursive optimal control problem. The delays are given as moving averages with respect to general finite measures and appear in all the coefficients of the control system. In particular, the final cost can contain the state delay. To derive the maximum principle, we introduce a new form of anticipated backward stochastic evolution equations with a terminal acting on an interval as adjoint equations of delay state equations, and deploy a proper dual analysis between them. Under certain convex assumptions, we also show the sufficiency of the maximum principle. |
|