Weak Error of Dean-Kawasaki Equation with Smooth Mean-Field Interactions

Abstract

We consider the weak-error rate of the SPDE approximation by regularized Dean-Kawasaki equation with Itô noise for particle systems with mean-field interactions both on the drift and the noise. The global existence and uniqueness of the corresponding SPDEs are established using the variational approach to SPDEs, and the weak-error rate is estimated using the technique of Kolmogorov equations on the space of probability measures. In particular, the rate derived in this paper coincides with that is the previous work arXiv:2212.11714, which considered free Brownian particles using Laplace duality.