We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset S of the Euclidean space . We assume the maps are monotone (with respect to a suitable partial order) and a ‘topological’ condition on the maps. Then, we prove the existence of a pullback random attractor whose distribution is the unique stationary measure of the random iteration, and we obtain the synchronisation of random orbits. As a consequence of the synchronisation phenomenon, a functional central limit theorem is established.

中文翻译：

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地图的随机迭代：渐近稳定性、同步和功能中心极限定理

我们研究了定义在欧几里德空间的连接封闭子集S上的连续映射的独立同分布随机迭代。我们假设地图是单调的（相对于合适的偏序）和地图上的“拓扑”条件。然后，我们证明了一个回拉随机吸引子的存在，它的分布是随机迭代的唯一平稳测度，我们获得了随机轨道的同步。由于同步现象，函数中心极限定理成立。