Criteria for transience and recurrence of regime-switching diffusion processes *

By Jinghai Shao. 2014

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We provide some criteria for recurrence of regime-switching diffusion processes using the theory of M-matrix and the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion processes in a finite space or in an infinite countable space are all studied in this work. Especially, we put forward a finite partition method to deal with switching processes in an infinite countable space. As an application, we study the recurrence of regime-switching Ornstein-Uhlenbeck process, and provide a necessary and sufficient condition for a kind of nonlinear regime-switching diffusion processes.

Subfields: Geometry and Topology, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/d402fd6a075ad7bf1c905d42a8054ea8c6f82ab5