Central Limit Theorems and Moderate Deviations for Stochastic Reaction-Diffusion Lattice Systems

This paper is concerned with the stochastic reaction-diffusion lattice systems defined on the entire set with both locally Lipschitz nonlinear drift and diffusion terms. The central limit theorem is derived for such infinite-dimensional stochastic systems. Moreover, the moderate deviation principle of solution processes is also established by the weak convergence method based on the variational representation of positive functionals of Brownian motion. The method relies on proving the convergence of the solutions of the controlled stochastic lattice systems.