Science and Education Publishing International Journal of Partial Differential Equations and Applications 2376-9556 4 2 2016 9 13 Random Exponential Attractor and Equilibrium for a Stochastic Reaction-diffusion Equation with Multiplicative Noise 25 31 EN Gang Wang School of Science, Hubei University of Technology, Wuhan, China IJPDEA2016422 10.12691/ijpdea-4-2-2 2016 4 15 2016 7 11 2016 9 11 In this paper, we present a result on existence of exponential attractors for abstract random dynamical systems, and then give a criterion for exponentially attractive property of random attractors. As an application, we first prove that the random dynamical system generated by a stochastic reaction-diffusion equation possesses a random exponential attractor. Then we show that the unique random equilibrium when the nonlinearity satisfies some restrictive condition is exactly an exponential attractor.