Stability and Recurrence of Regime-Switching Diffusion Processes
Stability and Recurrence of Regime-Switching Diffusion Processes
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DOI：
10.1137/140962905
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发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
J. Shao;F. Xi
中科院分区：
文献类型：
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作者：
J. Shao;F. Xi
给出了状态切换扩散过程稳定性的若干判据。本文研究了有限状态空间和无限可数状态空间中状态独立和状态依赖的状态切换扩散过程。我们提供了两种方法来处理无限可数状态空间中的切换过程。一种是基于非奇异m矩阵理论的有限划分方法。另一个是双线性形式的主特征值的应用。我们的方法可以处理线性和非线性状态切换扩散过程。此外，还利用主特征值方法研究了状态切换扩散过程的递归性。
We provide some criteria on the stability of regime-switching diffusion processes. Both the state-independent and state-dependent regime-switching diffusion processes with switching in a finite state space and an infinite countable state space are studied in this work. We provide two methods to deal with switching processes in an infinite countable state space. One is a finite partition method based on the nonsingular M-matrix theory. Another is an application of principal eigenvalue of a bilinear form. Our methods can deal with both linear and nonlinear regime-switching diffusion processes. Moreover, the method of principal eigenvalue is also used to study the recurrence of regime-switching diffusion processes.