This paper deals with invariant measures of fractional stochastic reaction–diffusion equations on unbounded domains with locally Lipschitz continuous drift and diffusion terms. We first prove the existence and regularity of invariant measures, and then show the tightness of the set of all invariant measures of the equation when the noise intensity varies in a bounded interval. We also prove that every limit of invariant measures of the perturbed systems is an invariant measure of the corresponding limiting system. Under further conditions, we establish the ergodicity and the exponentially mixing property of invariant measures.

中文翻译：

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无界域上分数阶随机反应扩散方程的极限测度和遍历性

本文讨论了具有局部 Lipschitz 连续漂移和扩散项的无界域上的分数随机反应扩散方程的不变测度。我们首先证明了不变测度的存在性和规律性，然后证明了当噪声强度在有界区间内变化时方程所有不变测度的集合的紧密度。我们还证明了扰动系统不变测度的每一个极限都是相应极限系统的不变测度。在进一步的条件下，我们建立了不变测度的遍历性和指数混合特性。