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Viscosity Solutions for Singular HJB Equations: BSDE Representations and Stochastic Control
We introduce a notion of viscosity solution for Hamilton--Jacobi--Bellman (HJB) equations with distributional drift, based on paracontrolled test functions and related through a Zvonkin transformation to classical viscosity theory. The equations considered are of the form \[ \left(\partial_t+\frac12
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