| Abstract: |
| This talk is based on joint work with Federica Masiero.
We discuss a stochastic maximum principle for controlled stochastic differential equations
with delay in the state, control-dependent noise, and non-convex control sets. The cost
functional may depend on both the present state and its weighted past through general finite
measures. In the regular case, where the delay measures admit square-integrable densities, the
problem can be reformulated as an infinite-dimensional stochastic evolution equation in a Hilbert
space, and necessary optimality conditions are derived through spike variation and first- and
second-order adjoint equations. For general finite measures, including pointwise delays, the
analysis combines anticipated backward stochastic differential equations with an approximation
procedure for the second-order term. This yields a stochastic maximum principle beyond the
convex setting and clarifies the role of infinite-dimensional methods in delay control problems. |
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