Regularisation by Gaussian rough path lifts of fractional Brownian motions

2024/12/02 by Dareiotis, Konstantinos, Gerencsér, Máté, Lê, Khoa +1 · 2 citations
#60H07 #60H50 #60L20 #60L90 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2412.01645

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-Hölder space C^α 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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