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Long-time behavior of Lévy-driven Ornstein–Uhlenbeck processes with regime switching

Part of: Special processes Markov processes

Published online by Cambridge University Press:  04 May 2020

Zhongwei Liao  and
Jinghai Shao Open the ORCID record for Jinghai Shao [Opens in a new window]
Zhongwei Liao*
Affiliation:
South China Normal University
Jinghai Shao*
Affiliation:
Tianjin University
*
*Postal address: South China Research Center for Applied Mathematics and Interdisciplinary Studies, South China Normal University, Guangzhou 510631, China. Email address: zhwliao@hotmail.com
**Postal address: Center for Applied Mathematics, Tianjin University, Tianjin 300072, China. Email address: shaojh@tju.edu.cn
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Abstract

We investigate the long-time behavior of the Ornstein–Uhlenbeck process driven by Lévy noise with regime switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the Ornstein–Uhlenbeck process driven simply by Brownian motion, whose stationary distribution must be light-tailed, both the jumps caused by the Lévy noise and the regime switching described by a Markov chain can derive the heavy-tailed property of the stationary distribution. The different role played by the Lévy measure and the regime-switching process is clearly characterized.

Keywords

Ornstein–Uhlenbeck processLévy processregime switchingrecurrence

MSC classification

Primary: 60J75: Jump processes
Secondary: 60K37: Processes in random environments 60J60: Diffusion processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 1 , March 2020 , pp. 266 - 279
Copyright
© Applied Probability Trust 2020

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Footnotes

Supported in part by NNSFS of China (nos. 11771327, 11701588, 11831014).

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