Asymptotically autonomous robustness of random attractors for stochastic nonlocal Ginzburg–Landau lattice systems driven by linear mixed white noise in weighted space

The focus of this paper is on the limiting dynamics of stochastic Ginzburg–Landau lattice systems with long-range interactions, driven by linear mixed white noise in weighted space. We first prove the existence and uniqueness of random attractors for these systems under suitable assumptions on the weight function and coupling parameters of long-range interactions. We then show these attractors are backward compact and asymptotically autonomous, respectively, as the time-dependent forcing term converges to its time-independent counterpart.