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arXiv · 2505.19787

Entropy-Cost Inequalities for McKean-Vlasov SDEs with Singular Interactions

Xing Huang·Panpan Ren·Feng-Yu Wang
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Abstract

For a class of McKean-Vlasov stochastic differential equations with singular interactions, which include the Coulomb/Riesz/Biot-Savart kernels as typical examples (Examples 2.1 and 2.2), we derive the well-posedness and regularity estimates by establishing the entropy-cost inequality. To measure the singularity of interactions, we introduce a new probability distance induced by local integrable functions, and estimate this distance for the time-marginal laws of solutions by using the Wasserstein distance of initial distributions. A key point of the study is to characterize the path space of time-marginal distributions for the solutions, by using local hyperbound estimates on diffusion semigroups.

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Xing Huang, Panpan Ren, Feng-Yu Wang. 2025-05-26. Entropy-Cost Inequalities for McKean-Vlasov SDEs with Singular Interactions. https://arxiv.org/abs/2505.19787

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