Regularization by noise for rough differential equations driven by Gaussian rough paths
Résumé
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 > 1 4 , we prove that the drift may be taken to be κ > 0 Hölder continuous and bounded for κ > 3 2 − 1 2H. A flow transform of the equation and Malliavin calculus for Gaussian rough paths are used to achieve such a result.
Domaines
Mathématiques [math]
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revision_round_2-hal_arxiv.pdf (736.82 Ko)
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