A $K$-rough path above the space-time fractional Brownian motion

Abstract

We construct a $K$-rough path above either a space-time or a spatial fractional Brownian motion, in any space dimension $d$. This allows us to provide an interpretation and a unique solution for the corresponding parabolic Anderson model, understood in the renormalized sense. We also consider the case of a spatial fractional noise.

This preprint is the result of splitting our original submission arXiv:2003.14367, which was slightly too long. The present preprint contains the construction of the Stratonovich solution