By investigating McKean-Vlasov SDEs, the order preservation and positive correlation are characterized for nonlinear Fokker-Planck equations. The main results recover the corresponding criteria on these properties established in [3, 5] for diffusion processes or linear Fokker-Planck equations.
The author greatefully acknowledge support by European Union through the ERC-AdG 694405"RicciBounds" and Alexander von Humboldt Foundation.
I would like to thank the referee and Professor Feng-Yu Wang and Jianhai Bao for helpful comments and corrections.
"Order preservation and positive correlation for nonlinear Fokker-Planck equation." Electron. Commun. Probab. 27 1 - 12, 2022. https://doi.org/10.1214/22-ECP466