Rough linear PDE's with discontinuous coefficients - existence of solutions via regularization by fractional Brownian motion

Abstract

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.

arXiv commentv2: change in definition 5.1 v3: corrected error regarding strong local non-determinism. Merged together with arXiv:1512.07274