Stability and random attractors for a reaction-diffusion equation with multiplicative noise

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Random attractors for stochastic reaction–diffusion equations on unbounded domains (2009, background): “Preliminaries and Abstract Results In this section, we first recall some basic concepts related to random attractors for RDS (see [1, 3, 5–8, 34] for more detail) and then give some abstract results on the existence of (L(R),H(R))-random attractors.”
A stochastic pitchfork bifurcation in a reaction-diffusion equation (2001, methodology): “By following the analysis in Caraballo et al. (2000) one can show that the flow in each of these subspaces has a positively invariant compact absorbing set, namely a bounded set in H1(D) with radius r(ω), where r(ω) is a tempered random variable.”
Fractal dimension of random attractor for stochastic non-autonomous damped wave equation with linear multiplicative white noise (2015, background): “Recently, the random attractors for autonomous and nonautonomous random dynamical systems have been studied widely since Crauel and Flandoli [8] established a criterion for the existence of a random attractor for an autonomous random dynamical systems, see [3-5, 7, 9, 10, 16, 24-27] and the referenc”
Existence and continuity of bi-spatial random attractors and application to stochastic semilinear Laplacian equations (2015, background): “This concept generalizes some common concepts of random attractors (see [8,14,15,17]) and tempered random attractors (see [3–5,7,30,31,34]).”