论文标题
$ \ mathbb {r}^{k} $上地图的随机迭代：渐近稳定性，同步和功能性中心极限定理
Random iterations of maps on $\mathbb{R}^{k}$: asymptotic stability, synchronization and functional central limit theorem
论文作者
论文摘要
我们研究了在欧几里得空间的连接封闭子集$ s $ $ \ mathbb {r}^{k} $上定义的连续图的独立和相同分布的随机迭代。我们假设地图是单调的（相对于合适的部分秩序）和地图上的“拓扑”条件。然后，我们证明了一个回值随机吸引子的存在，其分布是随机迭代的唯一固定度量，并且获得了随机轨道的同步。由于同步现象，建立了功能性中心极限定理。
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. 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 synchronization of random orbits. As a consequence of the synchronization phenomenon, a functional central limit theorem is established.
