Criteria for transience and recurrence of regime-switching diffusion processes

TL;DR

This paper establishes new criteria for determining when regime-switching diffusion processes are recurrent or transient, using matrix theory and spectral analysis, applicable to both finite and countable state spaces.

Contribution

It introduces on-off type criteria for recurrence and transience, extending existing results to nonlinear processes and employing a finite partition method for countable spaces.

Findings

Improved criteria for recurrence of linear regime-switching diffusions

On-off criteria for certain nonlinear regime-switching diffusions

Development of a finite partition method for countable state spaces

Abstract

We provide some on-off type criteria for recurrence and transience 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 and a countable space are both studied. We put forward a finite partition method to deal with switching process in a countable space. As an application, we improve the known criteria for recurrence of linear regime-switching diffusion processes, and provide an on-off type criterion for a kind of nonlinear regime-switching diffusion processes.