Uniformly valid estimate and central limit theorem for stochastic reaction-diffusion lattice systems

This paper is devoted to investigating stochastic reaction-diffusion lattice systems with small parameters defined over the entire integer set. Utilizing perturbation methods, we establish the uniformly valid estimate for higher-order approximation solutions of these stochastic systems. Furthermore, we explore the central limit theorem of higher-order series expansions of the solutions by examining pth moment convergence of solution processes. We illustrate it with applications and numerical simulations to Geometric Brownian Motion and Logistic model.