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Multidimensional Stable Driven McKean-Vlasov SDEs with Distributional Interaction Kernel: Critical Thresholds and Related Models

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arxiv 2302.09900 v2 pith:PEP6TCH4 submitted 2023-02-20 math.AP math.PR

P.-E Chaudru de Raynal (LMJL) , J.-F Jabir (HSE) , S Menozzi (LaMME) This is my paper · ORCID
classification math.APmath.PR
keywords stablecriticaldistributionaldriveninteractionkernelmckean-vlasovmodels
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In this work we continue to investigate well-posedness for stable driven McKean-Vlasov SDEs with distributional interaction kernel following the approach introduced in [8]. We specifically focus on the impact of the Besov smoothness of the initial condition and quantify how it affects the corresponding density estimates for the SDE. In particular, we manage to attain some critical thresholds allowing to revisit/address in a stable noise setting some concrete physical and biological models.

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  1. 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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