Existence of optimal controls under the strong formulation

Question

I'm reading a textbook that gives both a "weak" and "strong" formulation of optimal control (first is a control function, second is the whole space, filtration, Brownian motion, and function etc). The textbook has a theorem about existence of optimal controls for the weak formulation and makes explicit that the strong formulation is not equivalent to a classical control problem. However, no existence theorem is present for the strong formulation.