Regularisation by Gaussian rough path lifts of fractional Brownian motions
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912155661500416 |
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| author | Dareiotis, Konstantinos Gerencsér, Máté Lê, Khoa Ling, Chengcheng |
| author_facet | Dareiotis, Konstantinos Gerencsér, Máté Lê, Khoa Ling, Chengcheng |
| contents | 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 $H\in(1/3,1/2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularisation by Gaussian rough path lifts of fractional Brownian motions Dareiotis, Konstantinos Gerencsér, Máté Lê, Khoa Ling, Chengcheng Probability 60H50, 60H07, 60L20, 60L90 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 $H\in(1/3,1/2)$. |
| title | Regularisation by Gaussian rough path lifts of fractional Brownian motions |
| topic | Probability 60H50, 60H07, 60L20, 60L90 |
| url | https://arxiv.org/abs/2412.01645 |