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Wong–Zakai approximations of second-order stochastic lattice systems driven by additive white noise
Stochastics and Dynamics  (IF0.98),  Pub Date : 2021-06-15, DOI: 10.1142/s0219493721500507
Yiju Chen, Chunxiao Guo, Xiaohu Wang

In this paper, we study the Wong–Zakai approximations of a class of second-order stochastic lattice systems with additive noise. We first prove the existence of tempered pullback attractors for lattice systems driven by an approximation of the white noise. Then, we establish the upper semicontinuity of random attractors for the approximate system as the size of approximation approaches zero.