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Setup Let $\mathscr{H}$ be a separable Hilbert space, $\mathcal{X}\triangleq \langle \Omega,\mathscr{F},\mathscr{F}_t,\mathbb{P}\rangle$ be a stochastic base and $X_t$ be an $H$-valued stochastic ...

I want to extend the following stochastic optimal control problem with randomized feedback control to the continuous time case \begin{align} \text{minimize}\quad \mathbb{E}_{\mathbb{H}}&\bigg[\...