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Long time behavior of Levy-driven Ornstein-Uhlenbeck process with regime-switchin
Zhong-Wei Liao, Jinghai Shao · 2019-06-20 · via math.PR updates on arXiv.org

In this work we investigate the long time behavior of the Ornstein-Uhlenbeck process driven by Levy 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 Levy noise and regime-switching described by Markov chain can derive the heavy-tailed property of the stationary distribution. In this work, the different role played by Levy measure and regime-switching process is clearly characterized.

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