Stochastic parabolic system: homogenization in time-dependent potential and random fluctuations

Abstract We study the convergence of the solution to the parabolic system with time-dependent, zero-mean Gaussian potential. Depending on the decorrelation properties of the Gaussian potential, the spatial dimension, and the order of the elliptic operator, we prove that the solution to the parabolic system strongly converges to the deterministic solution of the homogenized system. Additionally, we also get
that the random fluctuation converges in distribution, after a certain scaling transformation, to the solution of the stochastic partial differential system with additive noise. Unlike the error term, the random fluctuation can asymptotically capture the stochasticity in the solution.