Path Dependent McKean-Vlasov SDEs with Hölder Continuous Diffusion

Abstract

In this paper, the well-posedness for one-dimensional path dependent McKean-Vlasov SDEs with $\alpha$($\alpha \ge \frac{1}{2}$)-Hölder 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.

18 pages