Abstract
We provide some on-off type criteria for recurrence of regime-switching diffusion processes using the theory of M-matrix, the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion processes in a finite space and an infinite countable space are both studied. Especially, we put forward a finite partition method to deal with switching process in an infinite countable space. As an application, we study the recurrence of regime-switching Ornstein-Uhlenbeck process, and provide an on-off type criterion for a kind of nonlinear regime-switching diffusion processes.
Citation
Jinghai SHAO. "Criteria for transience and recurrence of regime-switching diffusion processes." Electron. J. Probab. 20 1 - 15, 2015. https://doi.org/10.1214/EJP.v20-4018
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