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

We consider the weak-error rate of the SPDE approximation by regularized Dean-Kawasaki equation with Itô noise, for particle systems exhibiting mean-field interactions both in the drift and the noise terms. Global existence and uniqueness of solutions to the corresponding SPDEs are established via the variational approach to SPDEs. To estimate the weak error, we employ the Kolmogorov equation technique on the space of probability measures. This work generalizes previous results for independent Brownian particles — where Laplace duality was used. In particular, we recover the same weak error rate as in that setting. This paper builds on joint work with X. Ji., H. Kremp and  N.  Perkowski.