Regularization by noise for rough differential equations driven by Gaussian rough paths
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866911776651608064 |
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| author | Catellier, Rémi Duboscq, Romain |
| author_facet | Catellier, Rémi Duboscq, Romain |
| contents | We consider the rough differential equation with drift driven by a Gaussian geometric rough path. Under natural conditions on the rough path, namely non-determinism, and uniform ellipticity conditions on the diffusion coefficient, we prove path-by-path well-posedness of the equation for poorly regular drifts. In the case of the fractional Brownian motion $B^H$ for $H>\frac14$, we prove that the drift may be taken to be $κ>0$ Hölder continuous and bounded for $κ>\frac32 - \frac1{2H}$. A flow transform of the equation and Malliavin calculus for Gaussian rough paths are used to achieve such a result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_04251 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Regularization by noise for rough differential equations driven by Gaussian rough paths Catellier, Rémi Duboscq, Romain Probability We consider the rough differential equation with drift driven by a Gaussian geometric rough path. Under natural conditions on the rough path, namely non-determinism, and uniform ellipticity conditions on the diffusion coefficient, we prove path-by-path well-posedness of the equation for poorly regular drifts. In the case of the fractional Brownian motion $B^H$ for $H>\frac14$, we prove that the drift may be taken to be $κ>0$ Hölder continuous and bounded for $κ>\frac32 - \frac1{2H}$. A flow transform of the equation and Malliavin calculus for Gaussian rough paths are used to achieve such a result. |
| title | Regularization by noise for rough differential equations driven by Gaussian rough paths |
| topic | Probability |
| url | https://arxiv.org/abs/2207.04251 |