We consider two related linear PDE’s perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a regularizing effect on the equations in the sense that we can prove existence of solutions for almost all paths of the fractional Brownian motion.
"Rough linear PDE’s with discontinuous coefficients – existence of solutions via regularization by fractional Brownian motion." Electron. J. Probab. 25 1 - 33, 2020. https://doi.org/10.1214/20-EJP437