Regularization by noise for rough differential equations driven by Gaussian rough paths

Rémi Catellier; Romain Duboscq

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arXiv · 2207.04251

Regularization by noise for rough differential equations driven by Gaussian rough paths

Rémi Catellier·Romain Duboscq

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Abstract

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 $\kappa>0$ H\"older continuous and bounded for $\kappa>\frac32 - \frac1{2H}$. A flow transform of the equation and Malliavin calculus for Gaussian rough paths are used to achieve such a result.

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BibTeX RIS

Rémi Catellier, Romain Duboscq. 2022-07-09. Regularization by noise for rough differential equations driven by Gaussian rough paths. https://arxiv.org/abs/2207.04251

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