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<p>The log-Harnack inequality and Bismut formula are established for McKean–Vlasov SDEs with singularities in all (time, space, distribution) variables, where the drift satisfies an integrability condition in time–space, and the continuity in distribution may be weaker than Dini. The main results considerably improve the existing ones for the case where the drift is <i>L</i>-differentiable and Lipschitz continuous in distribution with respect to the 2-Wasserstein distance.</p>

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Log-Harnack inequality and Bismut formula for McKean–Vlasov SDEs with singularities in all variables

  • 期刊论文

  • 发表日期：

    2025年8月9日

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  • Xing Huang,
  • Feng-Yu Wang

摘要

The log-Harnack inequality and Bismut formula are established for McKean–Vlasov SDEs with singularities in all (time, space, distribution) variables, where the drift satisfies an integrability condition in time–space, and the continuity in distribution may be weaker than Dini. The main results considerably improve the existing ones for the case where the drift is L-differentiable and Lipschitz continuous in distribution with respect to the 2-Wasserstein distance.