Strong solutions to SDEs with singular drifts driven by fractional Brownian motions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914349352747008 |
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| author | Gu, Jiazhen Yu, Qian |
| author_facet | Gu, Jiazhen Yu, Qian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04303 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong solutions to SDEs with singular drifts driven by fractional Brownian motions Gu, Jiazhen Yu, Qian Probability 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. |
| title | Strong solutions to SDEs with singular drifts driven by fractional Brownian motions |
| topic | Probability |
| url | https://arxiv.org/abs/2602.04303 |