LAUSR

Abstract In this paper, we consider the higher-order Wong–Zakai approximations of the non-autonomous stochastic reaction–diffusion equation driven by additive/multiplicative white noises. The solutions between the approximation equation and stochastic reaction–diffusion equation are compared in higher-order spaces, in terms of the initial data. Based on these results and the known L 2 -upper semi-continuity, we prove that the random attractor of the approximation random system converges to that of the non-autonomous stochastic reaction–diffusion equation with additive/multiplicative white noises in L p ( R N ) ∩ H 1 ( R N ) when the size of the approximation shrinks to zero.