Random attractors for stochastic reaction-diffusion equations on unbounded domains

The existence of a pullback attractor is established for a stochastic reaction-diffusion equation oil all n-dimensional space. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears as spatially distributed temporal white noise, The reaction-diffusion equation is recast as a random dynamical system and asymptotic compactness for this is demonstrated by using uniform a priori estimates for far-field values of solutions. (C) 2008 Elsevier Inc. All rights reserved.