Adjoint matching objectives derived from the Stochastic Maximum Principle have critical points satisfying HJB stationarity conditions for SOC problems with control-dependent drift and diffusion.
When individual results require additional regularity (e.g.C2 for the second-order adjoint, orJ(u;·,·)∈C1,2 for the verification step), this is stated explicitly
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Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Control
Adjoint matching objectives derived from the Stochastic Maximum Principle have critical points satisfying HJB stationarity conditions for SOC problems with control-dependent drift and diffusion.