Quantitative propagation of chaos for particle systems with bounded kernels and multiplicative noise

We prove the quantitative propagation of chaos for stochastic particle systems with interaction in both the drift and the diffusion coefficients, provided the drift kernel is bounded and free of Lipschitz or smoothness assumptions. Our proof is based on the relative entropy framework of Jabin and Wang \cite{JW2018}, and applies and extends their work on the exponential laws of large numbers. We extend one of their exponential laws of large numbers from the drift to the diffusion kernel to handle the error term arising from multiplicative noise in the entropy evolution equation. Proving this extension relies on a dynamic combinatorial analysis.