Electronic Journal of Probability

Criteria for transience and recurrence of regime-switching diffusion processes

Jinghai SHAO

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 63, 15 pp.

Dates
Accepted: 12 June 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067169

Digital Object Identifier
doi:10.1214/EJP.v20-4018

Mathematical Reviews number (MathSciNet)
MR3361251

Zentralblatt MATH identifier
1327.60017

Subjects
Primary: 60A10: Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}
Secondary: 60J60: Diffusion processes [See also 58J65] 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Regime-switching diffusions M-Matrix Recurrence Ergodicity

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

SHAO, Jinghai. Criteria for transience and recurrence of regime-switching diffusion processes. Electron. J. Probab. 20 (2015), paper no. 63, 15 pp. doi:10.1214/EJP.v20-4018. https://projecteuclid.org/euclid.ejp/1465067169


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