Optimal Convergence of Slow–Fast Stochastic Reaction–Diffusion–Advection Equation with Hölder-Continuous Coefficients

This paper investigates a slow–fast stochastic reaction–diffusion–advection equation with Hölder-continuous coefficients, where the irregularity of the coefficients presents significant analytical challenges. Our approach fundamentally relies on techniques from Poisson equations in Hilbert spaces, through which we establish optimal strong convergence rates for the approximation of the averaged solution by the slow component. The key advantage that this paper presents is that the coefficients are merely Hölder continuous yet the optimal rate can still be obtained, which is crucial for subsequent central limit theorems and numerical approximations.