On well-posedness of stable-driven McKean-Vlasov stochastic differential equations with Besov interaction kernel of non-positive regularity

2025/10/18 by Anna Bahrii, Bahrii, Anna
Economics, Econometrics and Finance · Mathematics · #30H25 #35Q84 #60G52 #60H10 #60H50 #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2510.16452

openalex created_date 2025/09/30 · openalex publication_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We prove well-posedness results for time-inhomogeneous stable-driven McKean-Vlasov stochastic differential equations with a convolution drift where the interaction kernel belongs to some Lebesgue-Besov space. The novelty of this work is that we manage to go below -1 in space regularity for such a kernel. This is achieved under additional smoothness conditions on the initial data and divergence conditions on the kernel. The proof heavily relies on a suitable product rule in Besov space. We prove smoothing properties of the law, which allow us to have the drift in a Lebesgue-Besov space of non-positive regularity.

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