论文标题
比较定理和稳定性在过渡速率矩阵的扰动下用于制度开关过程
Comparison theorem and stability under perturbation of transition rate matrices for regime-switching processes
论文作者
论文摘要
建立了与状态依赖性方案开关扩散过程的比较定理，这使我们能够仅通过马尔可夫链来控制状态依赖性切换组件的演变。此外，还提供了对过渡速率矩阵扰动下马尔可夫政权转换过程的稳定性的敏锐估计。我们的方法是基于根据Skorokhod表示的精神进行切换过程的精心构造，根据所解决的问题而有所不同。特别是，这种方法可以应对无限状态空间中的切换过程，而不一定是出生死亡类型。作为一种应用，可以改善有关状态依赖性制度转换过程的成真和稳定性的一些已知结果。
A comparison theorem for state-dependent regime-switching diffusion processes is established, which enables us to control pathwisely the evolution of the state-dependent switching component simply by Markov chains. Moreover, a sharp estimate on the stability of Markovian regime-switching processes under the perturbation of transition rate matrices is provided. Our approach is based on the elaborate constructions of switching processes in the spirit of Skorokhod's representation theorem varying according to the problem being dealt with. In particular, this method can cope with the switching processes in an infinite state space and not necessarily being of birth-death type. As an application, some known results on ergodicity and stability of state-dependent regime-switching processes can be improved.
