论文标题
二维马尔可夫过程的稳定性，并应用于无限阶段的QBD过程
Stability of two-dimensional Markov processes, with an application to QBD processes with an infinite number of phases
论文作者
论文摘要
在本文中，我们得出了一个简单的漂移条件，可以使一类二维马尔可夫进程的稳定性，为此，其中一种坐标（也称为{\ em相位}为方便起见）具有良好的理解行为，取决于另一个坐标（也称为{\ em Level}）。第一个（相）组件的过渡可能取决于第二个成分，并且仅假定最终是独立的。第二个（级别）组件具有部分界限的跳跃，并且假定它具有负漂移，因为第一个（第一个是固定分布）。这项工作中介绍的结果可以应用于四分之一和半平面上的QBD（准生气和死亡）类型的过程，该过程相互依存。此外，它们提供了一种现成的技术来解决一类二维马尔可夫流程的稳定性问题。这些结果使垫脚石在文献中缩小了现有的差距，该文献是为二维过程提供了易于验证的条件/标准，这些过程具有无限的跳跃和两个组件之间的相互依存关系。
In this paper, we derive a simple drift condition for the stability of a class of two-dimensional Markov processes, for which one of the coordinates (also referred to as the {\em phase} for convenience) has a well understood behaviour dependent on the other coordinate (also referred as {\em level}). The first (phase) component's transitions may depend on the second component and are only assumed to be eventually independent. The second (level) component has partially bounded jumps and it is assumed to have a negative drift given that the first one is in its stationary distribution. The results presented in this work can be applied to processes of the QBD (quasi-birth-and-death) type on the quarter- and on the half-plane, where the phase and level are interdependent. Furthermore, they provide an off-the-shelf technique to tackle stability issues for a class of two-dimensional Markov processes. These results set the stepping stones towards closing the existing gap in the literature of deriving easily verifiable conditions/criteria for two-dimensional processes with unbounded jumps and interdependence between the two components.
