Path Dependent McKean-Vlasov SDEs with H\"{o}lder Continuous Diffusion

TL;DR

This paper establishes well-posedness and propagation of chaos for one-dimensional path-dependent McKean-Vlasov SDEs with Hölder continuous diffusion, advancing understanding of their stability and convergence properties.

Contribution

It provides new results on existence, uniqueness, and quantitative propagation of chaos for McKean-Vlasov SDEs with Hölder continuous diffusion, which were previously less understood.

Findings

Well-posedness of the SDEs under Hölder continuous diffusion.

Quantitative propagation of chaos in Wasserstein, total variation, and relative entropy.

Extension of classical results to path-dependent and less regular diffusion settings.

Abstract

In this paper, the well-posedness for one-dimensional path dependent McKean-Vlasov SDEs with $\alpha$($\alpha\geq \frac{1}{2}$)-H\"{o}lder continuous diffusion is investigated. Moreover, the associated quantitative propagation of chaos in the sense of Wasserstein distance, total variation distance as well as relative entropy is studied.