McKean-Vlasov stochastic equations with H\"older coefficients

TL;DR

This paper offers a simplified proof of the well-posedness of McKean-Vlasov stochastic equations with H"older coefficients, extending results to hypoelliptic PDEs using Gaussian estimates without measure derivatives.

Contribution

It provides a direct proof approach that relaxes previous assumptions and broadens applicability to hypoelliptic PDEs in McKean-Vlasov equations.

Findings

Streamlined proof of well-posedness for McKean-Vlasov equations

Extension to hypoelliptic PDEs under weaker conditions

Avoidance of derivatives with respect to the measure argument

Abstract

This work revisits the well-posedness of non-degenerate McKean-Vlasov stochastic differential equations with H\"older continuous coefficients, recently established by Chaudru de Raynal. We provide a streamlined and direct proof that leverages standard Gaussian estimates for uniformly parabolic PDEs, bypassing the need for derivatives with respect to the measure argument and extending applicability to hypoelliptic PDEs under weaker assumptions.