A central limit theorem for interacting diffusion processes is shown. The proof is based on an infinite-dimensional stochastic integral representation of smooth functionals of diffusion processes. Exponential decay of correlations and the equation of the fluctuation field are also obtained.
Jean-Dominique Deuschel. "Central Limit Theorem for an Infinite Lattice System of Interacting Diffusion Processes." Ann. Probab. 16 (2) 700 - 716, April, 1988. https://doi.org/10.1214/aop/1176991781