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math.PR updates on arXiv.org

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Regularisation by Gaussian rough path lifts of fractional Brownian motions
Konstantinos Dareiotis, Máté Gerencsér, Khoa Lê, Chengcheng Ling · 2024-12-02 · via math.PR updates on arXiv.org

The aim of the paper is to show the probabilistically strong well-posedness of rough differential equations with distributional drifts driven by the Gaussian rough path lift of fractional Brownian motion with Hurst parameter $H\in(1/3,1/2)$. We assume that the noise is nondegenerate and the drift lies in the Besov-Hölder space $\mathcal{C}^α$ for some $α>1-1/(2H)$. The latter condition matches the one of the additive noise case, thereby providing a multiplicative analogue of Catellier-Gubinelli in the regime $H\in(1/3,1/2)$.

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