We study forward asymptotic autonomy of a pullback random attractor for a non-autonomous random lattice system and establish the criteria in terms of convergence, recurrence, forward-pullback absorption and asymptotic smallness of the discrete random dynamical system. By applying the abstract result to both non-autonomous and autonomous stochastic lattice equations with random viscosity, we show the existence of both pullback and global random attractors such that the time-component of the pullback attractor semi-converges to the global attractor as the time-parameter tends to infinity.

中文翻译：

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具有随机粘度的随机晶格模型的渐近自主吸引子

我们研究了非自治随机晶格系统的回拉随机吸引子的前向渐近自治，并在离散随机动力系统的收敛、递归、前向回拉吸收和渐近小度方面建立了标准。通过将抽象结果应用于具有随机粘性的非自治和自治随机晶格方程，我们证明了回拉和全局随机吸引子的存在，使得回拉吸引子的时间分量半收敛到全局吸引子作为时间-参数趋于无穷大。