Regularisation by Gaussian rough path lifts of fractional Brownian motions
Abstract
The aim of the paper is to show the probabilistically strong well-posedness of rough differential equations with distributional drifts driven by the Gaussian rough path lift of fractional Brownian motion with Hurst parameter H∈(1/3,1/2). We assume that the noise is nondegenerate and the drift lies in the Besov-H\"older space Cα for some α>1-1/(2H). The latter condition matches the one of the additive noise case, thereby providing a multiplicative analogue of Catellier-Gubinelli in the regime H∈(1/3,1/2).
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