Large deviation principles of stochastic reaction-diffusion lattice systems with superlinear noise

In this paper, we study the large deviation principle of stochastic reaction-diffusion lattice systems defined on Zn when the nonlinear drift and diffusion terms both have a superlinear growth rate. We first prove the well-posedness and continuity of solutions to a controlled equation associated with the stochastic lattice system, and then establish the large deviation principle for the system by the weak convergence method.