Existence and upper semicontinuity of attractors for stochastic equations with deterministic non-autonomous terms

We prove the existence and uniqueness of tempered random attractors for stochastic Reaction–Diffusion equations on unbounded domains with multiplicative noise and deterministic non-autonomous forcing. We establish the periodicity of the tempered attractors when the stochastic equations are forced by periodic functions. We further prove the upper semicontinuity of these attractors when the intensity of stochastic perturbations approaches zero.