Work

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

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2506.11900

Authors: Anzeletti, Lukas, Galeati, Lucio, Richard, Alexandre, Tanré, Etienne

Institutions: TU Wien, University of L'Aquila, Centre National de la Recherche Scientifique, Université Paris-Saclay, CentraleSupélec, Institut national de recherche en sciences et technologies du numérique, Université Côte d'Azur, Laboratoire Jean-Alexandre Dieudonné

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W4415069736

Cites: 5

Cited by: 4

Related to: 10