Title
Regularisation by noise in rough differential equations
Abstract
We show strong well-posedness of rough differential equations with distributional drift driven by the Gaussian rough path lift of fractional Brownian motion with Hurst parameter $H\in(1/3,1/2)$.
The noise coefficient is uniformly elliptic and sufficiently regular while the drift is a distribution in the H\”older-Besov space $\mathcal{C}^\alpha$ with $\alpha>1-1/(2H)$. The latter condition matches the one of the additive noise setting from [Catellier-Gubinelli, 2016] thereby providing a complete multiplicative analogue. This is joint work (in progress) with M. Gerencsér, K. Lê, and C. Ling.