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Pré-Publication, Document De Travail Année : 2023

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.
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Dates et versions

hal-03723000 , version 1 (13-07-2022)
hal-03723000 , version 2 (27-10-2023)
hal-03723000 , version 3 (14-02-2024)

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Rémi Catellier, Romain Duboscq. Regularization by noise for rough differential equations driven by Gaussian rough paths. 2023. ⟨hal-03723000v2⟩
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