Uniform attractors for non-autonomous random dynamical systems

Several existence criteria for uniform attractors are given, and the relationship between uniform and cocycle attractors is carefully studied. To overcome the measurability difficulty, the symbol space is required to be Polish which is shown fulfilled by the hulls of Llocp(R;Lr) functions, p,r>1. Moreover, uniform attractors for continuous NRDS are shown determined by uniformly attracting deterministic compact sets. Finally, the uniform attractor for a stochastic reaction-diffusion equation with translation-bounded external forcing are studied as applications.