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Existence and uniqueness results for strongly degenerate McKean-Vlasov equations with rough coefficients

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arxiv 2409.14451 v1 pith:VBR5SQXX submitted 2024-09-22 math.PR

Andrea Pascucci , Alessio Rondelli , Alexander Yu Veretennikov This is my paper · ORCID
classification math.PR
keywords resultscoefficientsdegenerateequationsexistencemckean-vlasovroughweak
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We present existence results for weak solutions to a broad class of degenerate McKean-Vlasov equations with rough coefficients, expanding upon and refining the techniques recently introduced by the third author. Under certain structural conditions, we also establish results concerning both weak and strong well-posedness.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the density of singular SDEs with fractional noise and applications to McKean-Vlasov equations

    math.PR 2025-06 accept novelty 7.0 of 10

    Singular fBm-driven SDEs with distributional drifts have densities with Besov regularity and Gaussian tails, and the associated McKean-Vlasov equations are well-posed down to the subcritical scaling threshold.

  2. Well-posedness of kinetic McKean-Vlasov equations

    math.PR 2025-01 conditional novelty 7.0 of 10

    Kinetic McKean-Vlasov SDEs with Hölder coefficients and law-dependent diffusion are weakly well-posed under a weak Hörmander condition.

  3. McKean-Vlasov stochastic equations with H\"older coefficients

    math.PR 2024-12 conditional novelty 6.0 of 10

    Non-degenerate McKean-Vlasov SDEs with bounded α-Hölder coefficients have unique weak solutions, proven via a new fixed-point argument in a dual-Hölder metric on flows of marginal laws.

  4. McKean-Vlasov equations with singular coefficients - a review of recent results

    math.PR 2025-07 accept novelty 3.0 of 10

    This paper is a structured review of singular McKean-Vlasov SDEs, unifying the Lp-Lq and distributional drift frameworks and their main solution tools.

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