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

Aur\'elien Deya; Cheng Ouyang; Samy Tindel; Xia Chen

arxiv: 2009.03426 · v1 · pith:CAZK4Z37new · submitted 2020-09-07 · 🧮 math.PR

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

Xia Chen , Aur\'elien Deya , Cheng Ouyang , Samy Tindel This is my paper

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keywords fractionalabovebrownianmotionpathroughspace-timespatial

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

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