Diffusion approximation for multi-scale stochastic reaction-diffusion equations

In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit original system is obtained, where an extra Gaussian term appears. Such explicitly given in terms of solution Poisson Hilbert space. Moreover, also obtain rate convergence, and convergence shown not to depend on regularity coefficients respect variable, which coincides intuition since component has been totally homogenized out equation.