5 papers
Non-uniqueness for McKean--Vlasov SDEs with Hölder diffusion coefficients
Martin Bergerhausen, Paul Nikolaev, David J. Prömel
We show that uniqueness may fail for one-dimensional McKean--Vlasov stochastic differential equations with Hölder continuous diffusion coefficients. More precisely, for every \(α\i…
Convergence rate for Fluctuations of mean field interacting diffusion and application to 2D viscous Vortex model and Coulomb potential
Alekos Cecchin, Paul Nikolaev
For a system of mean field interacting diffusion on , the empirical measure converges to the solution of the Fokker-Planck equation. Refining this mean fiel…
Characterization of Besov spaces with dominating mixed smoothness by differences
Paul Nikolaev, David J. Prömel, Mathias Trabs
Besov spaces with dominating mixed smoothness, on the product of the real line and the torus as well as bounded domains, are studied. A characterization of these function spaces in…
Quantitative relative entropy estimates on the whole space for convolution interaction forces
Paul Nikolaev, David J. Prömel
Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting system…
Well-posedness of diffusion-aggregation equations with bounded kernels and their mean-field approximations
Li Chen, Paul Nikolaev, David J. Prömel
The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interact…