A $K$-rough path above the space-time fractional Brownian motion
Probability
2020-09-09 v1
Abstract
We construct a -rough path above either a space-time or a spatial fractional Brownian motion, in any space dimension . 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.
Keywords
Cite
@article{arxiv.2009.03426,
title = {A $K$-rough path above the space-time fractional Brownian motion},
author = {Xia Chen and Aurélien Deya and Cheng Ouyang and Samy Tindel},
journal= {arXiv preprint arXiv:2009.03426},
year = {2020}
}
Comments
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