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

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.