Strong solutions to SDEs with singular drifts driven by fractional Brownian motions

Abstract

In this paper, we establish the strong well-posedness of SDEs with merely integrable time-dependent drifts driven by fractional Brownian motions with Hurst parameter H<1/2. Our result holds over the entire subcritical regime and can be regarded as an extension of (Krylov and Rockner, Probab. Theory Relat. Fields, 131(2): 154-196 (2005)) to the fractional case. Furthermore, we prove the existence of stochastic flows of Sobolev diffeomorphisms for this class of SDEs, which generalizes a result in (Mohammed et al., Ann. Probab. 43, 1535-1576 (2015)). The approach adopted in our work is based on a compactness criterion for random fields in Wiener spaces.