Pullback Measures Attractors and Finite‐Dimensional Approximation for Nonlinearly Stochastic Plate Lattice Equations

ABSTRACT We study the existence and stability of pullback measure attractors for nonautonomous stochastic second‐order plate lattice equations with nonlinear noise. Using a different approach from the recent literature for other models, we construct a pullback measure attractor that pullback attracts all tempered bounded sets of probability measures. Moreover, we establish the finite‐dimensional approximation of the pullback measure attractor by truncated measure attractors under Hausdorff's semimetric between measure sets, it is crucial to prove the tightness of the union of null expansions of finite‐dimensional measure attractors.