Random attractor for stochastic reaction–diffusion equation with multiplicative noise on unbounded domains

Abstract In this paper we study the asymptotic dynamics for stochastic reaction–diffusion equation with multiplicative noise defined on unbounded domains. We investigate the existence of a random attractor for the random dynamical system associated with the equation. The asymptotic compactness of the random dynamical system is established by using uniform a priori estimates for far-field values of solutions and a cut-off technique.