Author

P. Friz

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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

Rough backward stochastic differential equations

We develop an intrinsic well-posedness theory for nonlinear backward stochastic differential equations (BSDEs) driven simultaneously by Brownian motion and a (level-$2$) rough path of finite $p$-variation. Unlike earlier approaches based on smooth approximation or transformation methods, we formulate the equation direc...

P. Friz, Jian Song, Hui-Lin Zhang et al. · 0 citations