| Abstract: |
| In this paper, we study the Pontryagin`s maximum principle for the stochastic recursive optimal control problem of a class of path-dependent stochastic evolution equations. In the control system, the state process depends on its past trajectory, the control is delayed via an integral with respect to a general finite measure, and the final cost relies on the delayed state. To obtain the maximum principle, we introduce a functional adjoint operator for the non-anticipative path derivative and establish the well-posedness of an anticipated backward stochastic evolution equation in the path-dependent form, which serves as the adjoint equation. |
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