Random attractors for non-autonomous stochasticwave equations with multiplicative noise

This paper is concerned with the asymptotic behaviorof solutionsof the damped non-autonomous stochastic wave equationsdriven by multiplicative white noise.We prove the existence of pullback random attractorsin H¹(Rⁿ) × L²(Rⁿ)when the intensity of noise is sufficiently small.We demonstrate that these random attractorsare periodic in time if so are the deterministic non-autonomousexternal terms.We also establish the upper semicontinuityof random attractors when the intensity of noise approaches zero.In addition, we prove the measurability of random attractorseven if the underlying probability space is not complete.