LAUSR

In this paper, we establish the existence of random attractors for stochastic parabolic equations driven by additive noise as well as deterministic non-autonomous forcing terms in weighted Lebesgue spaces \begin{document}$ L_{\delta}^r(\mathcal{O})$\end{document} , where \begin{document}$ 1 is the distance from \begin{document}$ x$\end{document} to the boundary. The nonlinearity \begin{document}$ f(x,u)$\end{document} of equation depending on the spatial variable does not have the bound on the derivative in \begin{document}$ u$\end{document} , and then causes critical exponent. In both subcritical and critical cases, we get the well-posedness and dissipativeness of the problem under consideration and, by smoothing property of heat semigroup in weighted space, the asymptotical compactness of random dynamical system corresponding to the original system.