论文标题
perron-frobenius定理，用于强烈的大量随机链
A Perron-Frobenius Theorem for Strongly Aperiodic Stochastic Chains
论文作者
论文摘要
我们将Perron-Frobenius定理推广到随时间变化的行式矩阵，如下所示：使用Kolmogorov的绝对概率序列的概念，这些概念是主要特征向往的时间变化的类似物，我们确定了一组连接条件，并确定了IR可及时性（强度连接）的概念（我们）的概念（我们的强度连接），我们（vary）是ir可及时的（我们）的仪式（我们）ir trice（vary）irs ir newsion n of time（与给定矩阵序列相关的绝对概率序列是（a）均匀的阳性和（b）唯一的。我们的结果适用于离散时间和连续时间设置。然后，我们将主要结果的一些应用程序与非基质学习，分布式优化，意见动力学以及对随机网络的平均动力学相关的应用。
We derive a generalization of the Perron-Frobenius theorem to time-varying row-stochastic matrices as follows: using Kolmogorov's concept of absolute probability sequences, which are time-varying analogs of principal eigenvectors, we identify a set of connectivity conditions that generalize the notion of irreducibility (strong connectivity) to time-varying matrices (networks), and we show that under these conditions, the absolute probability sequence associated with a given matrix sequence is (a) uniformly positive and (b) unique. Our results apply to both discrete-time and continuous-time settings. We then discuss a few applications of our main results to non-Bayesian learning, distributed optimization, opinion dynamics, and averaging dynamics over random networks.
