Weak and Wasserstein convergence of periodic measures of lattice plate equations driven by infinite-dimensional superlinear noise

We consider the convergence and existence of periodic measures of a broad category of stochastic lattice plate equations defined on ℤ . As the drift term is an arbitrary order polynomial growth rate and also the diffusion term has a family of locally Lipschitz continuous functions with superlinear growth rate, we certify that the system has a periodic measure. Without adding any additional conditions on the drift and diffusion terms, and we demonstrate that the union S ε of all periodic measures of this system corresponding to the noise intensity ε is tight, then the weak limit of every sequence 𝜇 𝜀 𝑚 ∈ 𝑆 𝜀 with 𝜀 𝑚 → ¯ 𝜀 must be a periodic measure of the system corresponding to the noise intensity ¯ 𝜀 . When the diffusion and drift terms are globally Lipschitz with linear growth rates, we further discuss the convergence of these probability measures under the Wasserstein distance of probability measures, and prove that the Wasserstein distance of μ ε ∈ S ε and 𝜇 𝜀 0 ∈ 𝑆 𝜀 0 is bounded by 𝑐 | 𝜀 − ⁢ 𝜀 0 | about the constant c independent of ε. The tightness of the probability distributions of solutions and also the union of periodic measures are proved through the use of the thoughts of uniform tail-estimates to conquer the shortage of compact embeddings in infinite-dimensional lattice systems.