Order Preservation and Positive Correlation for Nonlinear Fokker Planck Equations

TL;DR

This paper characterizes order preservation and positive correlation in nonlinear Fokker-Planck equations through McKean-Vlasov SDEs, extending known criteria from diffusion processes and linear equations.

Contribution

It provides new criteria for order preservation and positive correlation specifically for nonlinear Fokker-Planck equations, generalizing previous results.

Findings

Criteria for order preservation established

Criteria for positive correlation established

Results extend known properties from linear to nonlinear equations

Abstract

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.