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arXiv · 2009.03426

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

Xia Chen·Aurélien Deya·Cheng Ouyang·Samy Tindel
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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.

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Xia Chen, Aurélien Deya, Cheng Ouyang, Samy Tindel. 2020-09-07. A $K$-rough path above the space-time fractional Brownian motion. https://arxiv.org/abs/2009.03426

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