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

Lukas Anzeletti; Lucio Galeati; Alexandre Richard; Etienne Tanré

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arXiv · 2506.11900

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

Lukas Anzeletti·Lucio Galeati·Alexandre Richard·Etienne Tanré

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Abstract

We investigate properties of the (conditional) law of the solution to SDEs driven by fractional Brownian noise with a singular, possibly distributional, drift. Our results on the law are twofold: i) we quantify the spatial regularity of the law, while keeping track of integrability in time, and ii) we prove that it has a density with Gaussian tails. Then the former result is used to establish novel results on existence and uniqueness of solutions to McKean-Vlasov equations of convolutional type.

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Lukas Anzeletti, Lucio Galeati, Alexandre Richard, Etienne Tanré. 2025-06-13. On the density of singular SDEs with fractional noise and applications to McKean-Vlasov equations. https://arxiv.org/abs/2506.11900

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