We study the random dynamical system generated by a stochastic reaction-diffusion equation with additive noise on the whole space and prove the existence of an -random attractor for such a random dynamical system. The nonlinearity is supposed to satisfy the growth of arbitrary order (). The -asymptotic compactness of the random dynamical system is obtained by using an extended version of the tail estimate method introduced by Wang (1999) and the cut-off technique.
"-Random Attractors for Stochastic Reaction-Diffusion Equation on Unbounded Domains." Abstr. Appl. Anal. 2013 1 - 23, 2013. https://doi.org/10.1155/2013/279509