论文标题
马尔可夫操作员的广义涂布丁的牙刷系数和统一的奇迹
Generalized Dobrushin Ergodicity Coefficient and Uniform Ergodicities of Markov Operators
论文作者
论文摘要
在本文中，研究了作用于抽象状态空间的马尔可夫操作员的稳定性和扰动范围。在这里，抽象状态空间是一个有序的BANACH空间，该空间在正面的圆锥体上具有添加性属性。我们基本上通过所谓的普通多布鲁丁的牙周系数研究了马尔可夫操作员的统一厄贡特性。这使我们能够通过利率获得几个收敛结果。关于马尔可夫操作员的准紧凑性的一些结果证明了奇迹系数。此外，给出了均匀的$ p $ ergodic马尔可夫操作员的特征，这使我们能够构建很多类型的操作员的例子。马尔可夫操作员的均匀终身制是根据多布鲁什（Dobrushin）牙齿系数建立的。获得的结果在经典和量子设置中甚至是新的
In this paper the stability and the perturbation bounds of Markov operators acting on abstract state spaces are investigated. Here, an abstract state space is an ordered Banach space where the norm has an additivity property on the cone of positive elements. We basically study uniform ergodic properties of Markov operators by means of so-called a generalized Dobrushin's ergodicity coefficient. This allows us to get several convergence results with rates. Some results on quasi-compactness of Markov operators are proved in terms of the ergodicity coefficient. Furthermore, a characterization of uniformly $P$-ergodic Markov operators is given which enable us to construct plenty examples of such types of operators. The uniform mean ergodicity of Markov operators is established in terms of the Dobrushin ergodicity coefficient. The obtained results are even new in the classical and quantum settings
