论文标题
部分可观测时空混沌系统的无模型预测
Networks of reinforced stochastic processes: a complete description of the first-order asymptotics
论文作者
论文摘要
我们考虑了有限的加强随机过程集合，它们之间具有一般的基于网络的交互。我们提供了足够和必要的条件，以便具有某种几乎确定的渐近同步形式，这可以大致定义为相互作用过程行为的几乎确定的长期均匀化。具体而言，我们检测到完全同步的制度，其中所有过程都趋向于相同的随机变量，即系统几乎肯定会收敛的第二个制度，但是没有几乎确定渐近同步的形式，而系统没有严格的正概率收敛的另一个系统。在后一种情况下，根据相互作用矩阵的周期对系统进行分区，我们在循环类别中几乎确定了渐近同步，并且具有严格的积极概率，即这些类别的渐近周期性行为。
We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization, which could be roughly defined as the almost sure long-run uniformization of the behavior of interacting processes. Specifically, we detect a regime of complete synchronization, where all the processes converge toward the same random variable, a second regime where the system almost surely converges, but there exists no form of almost sure asymptotic synchronization, and another regime where the system does not converge with a strictly positive probability. In this latter case, partitioning the system in cyclic classes according to the period of the interaction matrix, we have an almost sure asymptotic synchronization within the cyclic classes, and, with a strictly positive probability, an asymptotic periodic behavior of these classes.
