Author

Dirk Becherer

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Preprint Sep 2026

A pathwise approach to semilinear SPDEs with L\'evy drivers

We extend the notion of robust viscosity solutions to semilinear rough partial differential equations (RPDEs) of the form \[ \partial_t u + \mathcal{L}_t u + f(t,x,u,\sigma^{\top}\nabla_x u) + h(t,x,u)\,\diamond dW = 0, \quad u(T,x)=\xi(x), \] driven by a discontinuous path $W$ of finite $q$-variation for some $q<2$. T...

Dirk Becherer, P. Friz, Yu-Chen Sun · 0 citations

Preprint Sep 2026

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\Delta+b\cdot\nabla\...

Dirk Becherer, Nicolas Perkowski, Yu-Chen Sun et al. · 0 citations