Higher-order Wong–Zakai approximations of stochastic reaction–diffusion equations on [formula omitted].

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. • Approximation is obtained in L p ∩ H 1 for equations with additive noise. • Approximation is obtained in L p ∩ H 1 for equations with multiplicative noises. • Upper semi-continuity w.r.t. the size of approximations is derived in L p ∩ H 1 . [ABSTRACT FROM AUTHOR]