Long time behavior of Levy-driven Ornstein-Uhlenbeck process with regime-switchin
Probability
2019-06-21 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1906.08426,
title = {Long time behavior of Levy-driven Ornstein-Uhlenbeck process with regime-switchin},
author = {Zhong-Wei Liao and Jinghai Shao},
journal= {arXiv preprint arXiv:1906.08426},
year = {2019}
}