Criteria for transience and recurrence of regime-switching diffusion processes

Jinghai Shao

doi:10.1214/ejp.v20-4018

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.

Highlights

Regime-switching diffusion processes have received much attention lately, and they can provide more realistic formulation for many applications such as biology, mathematical finance, etc
The regime-switching diffusion process studied in this work can be viewed as a number of diffusion processes modulated by a random switching device or as a diffusion process which lives in a random environment
In [13], we studied the ergodicity for RSDP in Wasserstein distance

Summary

Introduction

Regime-switching diffusion processes have received much attention lately, and they can provide more realistic formulation for many applications such as biology, mathematical finance, etc. These criteria are applied to study the recurrence of regime-switching Ornstein-Uhlenbeck processes. We apply these criteria to study the processes considered in [11]

Criteria for recurrence and transience

Criteria for transience and recurrence