| Abstract: |
| We introduce the notion transposition solution for a class of McKean-Vlasov backward stochastic partial differential equations, providing a flexible framework to establish well-posedness under low regularity conditions via duality methods. This approach is particularly suited to infinite-dimensional stochastic systems where the given filtration is not natural. As an application, we study optimal control problems governed by Mckean-Vlasov stochastic partial differential equations, in which the coefficient depend on bothe the state and its probability distribution. Within this framework, we derive first-order necessary optimal conditions in the form of a stochastic maximum principle, where he corresponding adjoint equations are characterized as BSPDEs in the transposition sense. |
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